the additivity of traces in triangulated categories abstract we explain a fundamental additivity theorem for euler characteristics and generalized trace maps in triangulated categories the proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation the refinement consists of several new axioms relating products and distinguished triangles the axioms hold in the examples and shed light on generalized homology and cohomology theories

idempotent completion of triangulated categories we show that the idempotent completion of a triangulated category has a natural structure of a triangulated category the idempotent completion of the bounded derived category of an exact category gives the derived category of the idempotent completion in particular the derived category of an idempotent complete exact category is idempotent complete

classifying thick subcategories of the stable category of cohen macaulay modules abstract various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics in this paper as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p group due to benson carlson and rickard we consider classifying thick subcategories of the stable category of cohen macaulay modules over a gorenstein local ring the main result of this paper yields a complete classification of the thick subcategories of the stable category of cohen macaulay modules over a local hypersurface in terms of specialization closed subsets of the prime ideal spectrum of the ring which are contained in its singular locus

the spectrum of prime ideals in tensor triangulated categories we define the spectrum of a tensor triangulated category k as the set of so called prime ideals endowed with a suitable topology in this very generality the spectrum is the universal space in which one can define supports for objects of k this construction is functorial with respect to all tensor triangulated functors several elementary properties of schemes hold for such spaces e g the existence of generic points or some quasi compactness locally trivial morphisms are proved to be nilpotent we establish in complete generality a classification of thick ideal subcategories in terms of arbitrary unions of closed subsets with quasi compact complements thomason s theorem for schemes mutatis mutandis we also equip this spectrum with a sheaf of rings turning it into a locally ringed space we compute examples and show that our spectrum unifies the schemes of algebraic geometry and the support varieties of modular representation theory

three dimensional antiferromagnetic q state potts models application of the wang landau algorithm we apply a newly proposed monte carlo method the wang landau algorithm to the study of the three dimensional antiferromagnetic q state potts models on a simple cubic lattice we systematically study the phase transition of the models with q 3 4 5 and 6 we obtain the finite temperature phase transition for q 3 and 4 whereas the transition temperature is down to zero for q 5 for q 6 there exists no order for any temperature we also study the ground state properties the size dependence of the ground state entropy is investigated we find that the ground state entropy is larger than the contribution from the typical configurations of the broken sublattice symmetry state for q 3 the same situations are found for q 4 5 and 6

crossover and self averaging in the two dimensional site diluted ising model application of probability changing cluster algorithm using the newly proposed probability changing cluster pcc monte carlo algorithm we simulate the two dimensional 2d site diluted ising model since we can tune the critical point of each random sample automatically with the pcc algorithm we succeed in studying the sample dependent t c l and the sample average of physical quantities at each t c l systematically using the finite size scaling fss analysis for t c l we discuss the importance of corrections to fss both in the strong dilution and weak dilution regions the critical phenomena of the 2d site diluted ising model are shown to be controlled by the pure fixed point the crossover from the percolation fixed point to the pure ising fixed point with the system size is explicitly demonstrated by the study of the binder parameter we also study the distribution of critical temperature t c l its variance shows the power law l dependence l ensuremath n and the estimate of the exponent n is consistent with the prediction of aharony and harris phys rev lett 77 3700 1996 calculating the relative variance of critical magnetization at the sample dependent t c l we show that the 2d site diluted ising model exhibits weak self averaging

monte carlo analysis of the critical properties of the two dimensional randomly bond diluted ising model via wang landau algorithm abstract the influence of random bond dilution on the critical properties of the two dimensional ising model on a square lattice with periodic boundary conditions is presented using the monte carlo process with wang landau sampling the lattice linear size is l 20 140 and the concentration of the diluted bonds spans a wide range from weak to strong dilution namely q 0 05 0 1 0 2 0 3 0 4 the respective percolation limit for the square lattice is q c p e r c 0 5 its pure version q 0 has a second order phase transition with vanishing specific heat critical exponent an example of inapplicability of the harris criterion the main effort is focused on the temperature dependence of the specific heat and magnetic susceptibility to estimate the respective maximum values and subsequent pseudocritical temperatures for extracting the relative critical exponents we have also looked at the probability distribution of the susceptibility pseudocritical temperature and specific heat for assessing self averaging the study is carried out in the appropriately restricted but dominant energy subspaces by applying the finite size scaling analysis the critical exponents are estimated the specific heat exponent vanishes the correlation length exponent is equal to one and the critical exponents ratio retains its pure ising model value thus supporting the strong universality hypothesis

detecting cohomology for lie superalgebras abstract in this paper we use invariant theory to develop the notion of cohomological detection for type i classical lie superalgebras in particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller subalgebras these results are used later to affirmatively answer questions which were originally posed in boe et al 2010 5 and bagci et al 2008 2 about realizing support varieties for lie superalgebras via rank varieties constructed for the smaller detecting subalgebras

determining the density of states for classical statistical models a random walk algorithm to produce a flat histogram we describe an efficient monte carlo algorithm using a random walk in energy space to obtain a very accurate estimate of the density of states for classical statistical models the density of states is modified at each step when the energy level is visited to produce a flat histogram by carefully controlling the modification factor we allow the density of states to converge to the true value very quickly even for large systems from the density of states at the end of the random walk we can estimate thermodynamic quantities such as internal energy and specific heat capacity by calculating canonical averages at any temperature using this method we not only can avoid repeating simulations at multiple temperatures but we can also estimate the free energy and entropy quantities that are not directly accessible by conventional monte carlo simulations this algorithm is especially useful for complex systems with a rough landscape since all possible energy levels are visited with the same probability as with the multicanonical monte carlo technique our method overcomes the tunneling barrier between coexisting phases at first order phase transitions in this paper we apply our algorithm to both first and second order phase transitions to demonstrate its efficiency and accuracy we obtained direct simulational estimates for the density of states for two dimensional ten state potts models on lattices up to 200 x 200 and ising models on lattices up to 256 x 256 our simulational results are compared to both exact solutions and existing numerical data obtained using other methods applying this approach to a three dimensional j spin glass model we estimate the internal energy and entropy at zero temperature and using a two dimensional random walk in energy and order parameter space we obtain the rough canonical distribution and energy landscape in order parameter space preliminary data suggest that the glass transition temperature is about 1 2 and that better estimates can be obtained with more extensive application of the method this simulational method is not restricted to energy space and can be used to calculate the density of states for any parameter by a random walk in the corresponding space

universal finite size scaling functions with exact nonuniversal metric factors using exact partition functions and finite size corrections for the ising model on finite square plane triangular and honeycomb lattices and extending a method j phys 19 l1215 1986 to subtract leading singular terms from the free energy we obtain universal finite size scaling functions for the specific heat internal energy and free energy of the ising model on these lattices with exact nonuniversal metric factors

support varieties an axiomatic approach we provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category where the tensor product is not necessarily symmetric this is illustrated by examples taken in particular from the representation theory of finite dimensional algebras

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

reconstructing projective schemes from serre subcategories abstract given a positively graded commutative coherent ring a j 0 a j finitely generated as an a 0 algebra a bijection between the tensor serre subcategories of qgra and the set of all subsets y proj a of the form y i y i with quasi compact open complement proj a y i for all i is established to construct this correspondence properties of the ziegler and zariski topologies on the set of isomorphism classes of indecomposable injective graded modules are used in an essential way also there is constructed an isomorphism of ringed spaces proj a o proj a spec qgr a o qgr a where spec qgr a o qgr a is a ringed space associated to the lattice l serre qgr a of tensor serre subcategories of qgra

free fermions and the alexander conway polynomial we show how the conway alexander polynomial arises from theq deformation of z2 graded sl n n algebras in the simplestsl 1 1 case we then establish connection between classical knot theory and its modern versions based on quantum groups we first shown how the crystal and the fundamental group of the complement of a knot give rise naturally to the burau representation of the braid group the burau matrix is then transformed into theu q sl 1 1 r matrix by going to the exterior power algebra using a det str identity this allows us to recover the state model of k2 89 as well we also show how theu q sl 1 1 algebra describes free fermions propagating on the knot diagram we rewrite the conway alexander polynomial as a berezin integral and thus as an apparently new determinant

lack of self averaging of the specific heat in the three dimensional random field ising model we apply the recently developed critical minimum energy subspace scheme for the investigation of the random field ising model we point out that this method is well suited for the study of this model the density of states is obtained via the wang landau and broad histogram methods in a unified implementation by employing the n fold version of the wang landau scheme the random fields are obtained from a bimodal distribution h i ifmmode pm else textpm fi 2 and the scaling of the specific heat maxima is studied on cubic lattices with sizes ranging from l 4 to l 32 observing the finite size scaling behavior of the maxima of the specific heats we examine the question of saturation of the specific heat the lack of self averaging of this quantity is fully illustrated and it is shown that this property may be related to the question mentioned above

universality class of the two dimensional site diluted ising model in this work we evaluate the probability distribution function of the order parameter for the two dimensional site diluted ising model extensive monte carlo simulations have been performed for different spin concentrations p 0 70 ensuremath le p ensuremath le 1 on square lattices with linear sizes l 20 ensuremath le l ensuremath le 100 the results indicate that the universality class of the diluted ising model seems to be independent of the amount of dilution logarithmic corrections of the finite size critical temperature behavior of the model can also be inferred even for such small lattices

entropic sampling of simple polymer models within wang landau algorithm in this paper we apply a new simulation technique proposed in wang and landau wl 2001 phys rev lett 86 2050 to sampling of three dimensional lattice and continuous models of polymer chains distributions obtained by homogeneous unconditional random walks are compared with results of entropic sampling es within the wl algorithm while homogeneous sampling gives reliable results typically in the range of 4 5 orders of magnitude the wl entropic sampling yields them in the range of 20 30 orders and even larger with comparable computer effort a combination of homogeneous and wl sampling provides reliable data for events with probabilities down to 10 35 for the lattice model we consider both the athermal case self avoiding walks saws and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self avoiding walk for short chains the simulation results are checked by comparison with the exact data in wl calculations for chain lengths up to n 300 scaling relations for saws are well reproduced in the thermal case distribution over the number of contacts is obtained in the n range up to n 100 and the canonical averages internal energy heat capacity excess canonical entropy mean square end to end distance are calculated as a result in a wide temperature range the continuous model is studied in the athermal case by sorting conformations of a continuous phantom freely joined n bonded chain with a unit bond length over a stochastic variable the minimum distance between nonbonded beads we determine the probability distribution for the n bonded chain with hard sphere monomer units over its diameter a in the complete diameter range 0 a 2 within a single es run this distribution provides us with excess specific entropy for a set of diameters a in this range calculations were made for chain lengths up to n 100 and results were extrapolated to n for a in the range 0 a 1 25

logarithmic corrections to correlation decay in two dimensional random bond ising systems the statistics of critical spin spin correlation functions in ising systems with nonfrustrated disorder are investigated on a strip geometry via numerical transfer matrix techniques conformal invariance concepts are used in order to test for logarithmic corrections to pure power law decay against distance fits of our data to conformal invariance expressions specific to logarithmic corrections to correlations on strips give results with the correct sign for the moments of order n 0 ensuremath 4 of the correlation function distribution we find an interval of disorder strength along which corrections to pure system behavior can be decomposed into the product of a known n dependent factor and an approximately n independent one in accordance with predictions a phenomenological fitting procedure is proposed which takes partial account of subdominant terms of correlation function decay on strips in the low disorder limit it gives results in fairly good agreement with theoretical predictions provided that an additional assumption is made

finite size scaling analysis of the critical behavior of the baxter wu model abstract we use the recently developed critical minimum energy subspace crmes approximation scheme to study the critical behavior of the baxter wu model this scheme uses only a properly determined part of the energy spectrum and allows us to obtain high accuracy for relatively large systems with considerably reduced computational effort the density of states is constructed by a multi range wang landau sampling and from this we obtain the critical properties of specific heat and of the reduced binder cummulant the good agreement of our results with existing exact solutions demonstrates the accuracy of our approximation technique

the random field ising model with an asymmetric and anisotropic bimodal probability distribution abstract the ising model in the presence of a random field drawn from the asymmetric and anisotropic trimodal probability distribution p h i p h i h 0 q h i h 0 r h i is investigated the partial probabilities p q r take on values within the interval 0 1 consistent with the constraint p q r 1 asymmetric distribution h i is the random field variable with basic absolute value h 0 strength is the competition parameter which is the ratio between the respective strength of the random magnetic field in the two principal directions z and z and is positive so that the random fields are competing anisotropic distribution this probability distribution is an extension of the bimodal one allowing for the existence in the lattice of non magnetic particles or vacant sites the current random field ising system displays mainly second order phase transitions which for some values of p q and h 0 are followed by first order phase transitions joined smoothly by a tricritical point occasionally two tricritical points appear implying another second order phase transition in addition to these points re entrant phenomena can be seen for appropriate ranges of the temperature and random field for specific values of p and q using the variational principle we write down the equilibrium equation for the magnetization and solve it for both phase transitions and at the tricritical point in order to determine the magnetization profile with respect to h 0 considered as an independent variable in addition to the temperature

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

finite size scaling of the three dimensional conserved order parameter ising model via wang landau algorithm abstract the critical properties of the conserved order parameter cop version of the three dimensional ising model with zero magnetization were investigated by means of the monte carlo mc wang landau algorithm the study was carried out in appropriate restricted but dominant energy subspaces the main effort was focused on the specific heat and binder energy cumulant by using the density of states of the model for lattices with linear size l 4 60 by applying finite size scaling analysis the estimated values for the thermal critical exponent y t and critical temperature k c are in agreement with the considered as best values leading to the conclusion that this model belongs to the ising universality class the analysis revealed the necessity of corrections to scaling functions for interpreting correctly the mc data

softening of first order transition in three dimensions by quenched disorder we study by extensive monte carlo simulations the effect of random bond dilution on the phase transition of the three dimensional four state potts model that is known to exhibit a strong first order transition in the pure case the phase diagram in the dilution temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes in the strongly disordered regime numerical evidence for softening to a second order transition induced by randomness is given here a large scale finite size scaling analysis made difficult due to strong crossover effects presumably caused by the percolation fixed point is performed

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

high temperature series analysis of the free energy and susceptibility of the 2d random bond ising model abstract we derive high temperature series expansions for the free energy and susceptibility of the two dimensional random bond ising model with a symmetric bimodal distribution of two positive coupling strengths j1 and j2 and study the influence of the quenched random bond disorder on the critical behavior of the model by analysing the series expansions over a wide range of coupling ratios j2 j1 covering the crossover from weak to strong disorder we obtain for the susceptibility with two different methods compelling evidence for a singularity of the form t 7 4 ln t 7 8 as predicted theoretically by shalaev shankar and ludwig for the specific heat our results are less convincing but still compatible with the theoretically predicted log log singularity

critical behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

universal dependence on disorder of two dimensional randomly diluted and random bond j ising models we consider the two dimensional randomly site diluted ising model and the random bond j ising model also called the edwards anderson model and study their critical behavior at the paramagnetic ferromagnetic transition the critical behavior of thermodynamic quantities can be derived from a set of renormalization group equations in which disorder is a marginally irrelevant perturbation at the two dimensional ising fixed point we discuss their solutions focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder then we present a finite size scaling analysis of high statistics monte carlo simulations the numerical results confirm the renormalization group predictions and in particular the universality of the logarithmic corrections to the ising behavior due to quenched dilution

the sherrington kirkpatrick spin glass model in the presence of a random field with a joint gaussian probability density function for the exchange interactions and random fields abstract the magnetic systems with disorder form an important class of systems which are under intensive studies since they reflect real systems such a class of systems is the spin glass one which combines randomness and frustration the sherrington kirkpatrick ising spin glass with random couplings in the presence of a random magnetic field is investigated in detail within the framework of the replica method the two random variables exchange integral interaction and random magnetic field are drawn from a joint gaussian probability density function characterized by a correlation coefficient the thermodynamic properties and phase diagrams are studied with respect to the natural parameters of both random components of the system contained in the probability density the de almeida thouless line is explored as a function of temperature and other system parameters the entropy for zero temperature as well as for non zero temperatures is partly negative or positive acquiring positive branches as h 0 increases

on the derived category of a graded commutative noetherian ring abstract for any graded commutative noetherian ring where the grading group is abelian and where commutativity is allowed to hold in a quite general sense we establish an inclusion preserving bijection between on the one hand the twist closed localizing subcategories of the derived category and on the other hand subsets of the homogeneous spectrum of prime ideals of the ring we provide an application to weighted projective schemes

effective field theory for the ising model with a fluctuating exchange integral in an asymmetric bimodal random magnetic field a differential operator technique abstract the spin 1 2 ising model on a square lattice with fluctuating bond interactions between nearest neighbors and in the presence of a random magnetic field is investigated within the framework of the effective field theory based on the use of the differential operator relation the random field is drawn from the asymmetric and anisotropic bimodal probability distribution p h i p h i h 1 q h i c h 1 where the site probabilities p q take on values within the interval 0 1 with the constraint p q 1 h i is the random field variable with strength h 1 and c the competition parameter which is the ratio of the strength of the random magnetic field in the two principal directions z and z c is considered to be positive resulting in competing random fields the fluctuating bond is drawn from the symmetric but anisotropic bimodal probability distribution p j i j 1 2 j i j j j i j j where j and represent the average value and standard deviation of j i j respectively we estimate the transition temperatures phase diagrams for various values of the system s parameters c p h 1 susceptibility and equilibrium equation for magnetization which is solved in order to determine the magnetization profile with respect to t and h 1

thick subcategories of modules over commutative noetherian rings with an appendix by srikanth iyengar for a commutative noetherian ring a we compare the support of a complex of a modules with the support of its cohomology this leads to a classification of all full subcategories of a modules which are thick that is closed under taking kernels cokernels and extensions and closed under taking arbitrary direct sums in addition subcategories of a modules that are closed under taking submodules extensions and direct unions are classified via associated prime ideals

new monte carlo algorithm entropic sampling we present a new monte carlo sampling algorithm with which one can obtain any desired distribution of the sampling in one monte carlo simulation the free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm the main idea is to sample directly the entropy of a system at infinite temperature importance sampling is shown to be a particular case of the new algorithm the algorithm is tested against the exact partition function of the ital l 4 simple cubic ising model a comparison with the multicanonical ensemble for the ital l 12 ital q 10 potts model shows that the new algorithm is more general and more efficient

critical exponents of the dilute ising model from four loop expansions four loop expansions of the coefficients of the callan symanzik equation for 3d and 2d dilute ising models are calculated fixed point coordinates and critical exponents are estimated by two methods of summation of double series a generalisation of the pade borel approximation and the first confluent form of the e algorithm of wynn summation of the double series for the 2d dilute ising model gives exponents very close to exponents of the pure ising model in accordance with the exact solution

derived equivalences for hereditary artin algebras we study the role of the serre functor in the theory of derived equivalences let a a be an abelian category and let u v u v be a t structure on the bounded derived category d b a d b a with heart h h we investigate when the natural embedding h d b a h d b a can be extended to a triangle equivalence d b h d b a d b h d b a our focus of study is the case where a a is the category of finite dimensional modules over a finite dimensional hereditary algebra in this case we prove that such an extension exists if and only if the t structure is bounded and the aisle u u of the t structure is closed under the serre functor

monoidal infinity category of complexes from tannakian viewpoint in this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infty categories of quasi coherent complexes it can be viewed as a derived analogue of tannaka duality as a consequence we deduce that an algebraic stack satisfying a certain condition can be recovered from the symmetric monoidal stable infty category of quasi coherent complexes with tensor operation

q magnetism at roots of unity the authors study the thermodynamic properties of a family of integrable 1d spin chain hamiltonians associated with quantum groups at roots of unity these hamiltonians depend for each primitive root of unity on a parameter s which plays the role of a continuous spin the model exhibits ferromagnetism even though the interaction involved is between nearest neighbours the latter phenomenon is interpreted as a genuine quantum group effect with no classical analogue the discussion of conformal properties is given

scaling relations for logarithmic corrections multiplicative logarithmic corrections to scaling are frequently encountered in the critical behavior of certain statistical mechanical systems here a lee yang zero approach is used to systematically analyze the exponents of such logarithms and to propose scaling relations between them these proposed relations are then confronted with a variety of results from the literature

estimation of critical behavior from the density of states in classical statistical models we present a simple and efficient approximation scheme which greatly facilitates the extension of wang landau sampling or similar techniques in large systems for the estimation of critical behavior the method presented in an algorithmic approach is based on a very simple idea familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem it is illustrated that we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve the accuracy of critical parameters it is proposed that the extensions of the finite size critical part of the energy space determining the specific heat satisfy a scaling law involving the thermal critical exponent the method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic ising lattices the proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space the density of states of the zero field ising model on these lattices is obtained via a multirange wang landau sampling

galois theory of thick subcategories in modular representation theory abstract d j benson j f carlson and j rickard 1997 fund math 153 59 80 classified the tensor closed thick subcategories of finite dimensional representations of finite groups over algebraically closed fields in this paper we remove the algebraically closed hypothesis by applying some galois theory our methods apply more generally to finite dimensional cocommutative hopf algebras over a field thus they allow us to drop the algebraically closed hypothesis in the classification of thick subcategories of modules over finite dimensional sub hopf algebras of the steenrod algebra as well

self consistent scaling theory for logarithmic correction exponents multiplicative logarithmic corrections frequently characterize critical behavior in statistical physics here a recently proposed theory relating the exponents of such terms is extended to account for circumstances which often occur when the leading specific heat critical exponent vanishes also the theory is widened to encompass the correlation function the new relations are then confronted with results from the literature and some new predictions for logarithmic corrections in certain models are made

intertwiner realization of a simple non standard r matrix using jimbo s method we realize the non standard r matrix r12 1 2 x y as an intertwiner between non generic irreducible representations of the quantum affine algebra uq sl2

effect of random impurities on fluctuation driven first order transitions we analyse the effect of quenched uncorrelated randomness coupling to the local energy density of a model consisting of n coupled two dimensional ising models for n 2 the pure model exhibits a fluctuation driven first order transition characterized by runaway renormalization group behaviour we show that the addition of weak randomness acts to stabilize these flows in such a way that the trajectories ultimately flow back towards the pure decoupled ising fixed point with the usual critical exponents apart from logarithmic corrections we also show by examples that in higher dimensions such transitions may either become continuous or remain first order in the presence of randomness

entropic sampling via wang landau random walks in dominant energy subspaces dominant energy subspaces of statistical systems are defined with the help of restrictive conditions on various characteristics of the energy distribution such as the probability density and the fourth order binder s cumulant our analysis generalizes the ideas of the critical minimum energy subspace crmes technique applied previously to study the specific heat s finite size scaling here we illustrate alternatives that are useful for the analysis of further finite size anomalies and the behavior of the corresponding dominant subspaces is presented for the two dimensional 2d baxter wu and the 2d and 3d ising models in order to show that a crmes technique is adequate for the study of magnetic anomalies we study and test simple methods which provide the means for an accurate determination of the energy order parameter e m histograms via wang landau random walks the 2d ising model is used as a test case and it is shown that high level wang landau sampling schemes yield excellent estimates for all magnetic properties our estimates compare very well with those of the traditional metropolis method the relevant dominant energy subspaces and dominant magnetization subspaces scale as expected with exponents alpha nu and gamma nu respectively using the metropolis method we examine the time evolution of the corresponding dominant magnetization subspaces and we uncover the reasons behind the inadequacy of the metropolis method to produce a reliable estimation scheme for the tail regime of the order parameter distribution

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

critical behavior induced by quenched disorder abstract domain arguments and renormalization group calculations indicate that all temperature driven symmetry breaking first order phase transitions are converted to second order by quenched bond randomness this occurs for infinitesimal randomness in d 2 or d 4 respectively for discrete or continuous n 1 or n 2 component microscopic degrees of freedom even strongly first order transitions undergo this conversion to second order above these dimensions this conversion still occurs but requires a threshold bond randomness presumably with an intervening new tricritical point for example q state potts transitions can be made second order for any q in any d via bond randomness non symmetry breaking temperature driven first order transitions are eliminated under the above conditions these quenched fluctuation induced second order phase transitions suggest the possibility of new universality classes of criticality and tricriticality

exact finite size scaling corrections to the critical two dimensional ising model on a torus we analyse the finite size corrections to the energy and specific heat of the critical two dimensional spin ising model on a torus we extend the analysis of ferdinand and fisher to compute the correction of order l 3 to the energy and the corrections of order l 2 and l 3 to the specific heat we also obtain general results on the form of the finite size corrections to these quantities only integer powers of l 1 occur unmodified by logarithms except of course for the leading log l term in the specific heat and the energy expansion contains only odd powers of l 1 in the specific heat expansion any power of l 1 can appear but the coefficients of the odd powers are proportional to the corresponding coefficients of the energy expansion

critical behavior of the two dimensional spin diluted ising model via the equilibrium ensemble approach the equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two dimensional ising model in the presence of quenched random site dilution the numerical transfer matrix technique in semi infinite strips of finite width together with phenomenological renormalization and conformal invariance is particularly suited to putting the equilibrium ensemble approach to work a method by which to extract with great precision the critical temperature of the model is proposed and applied a more systematic finite size scaling analysis than in previous numerical studies has been performed a parallel investigation along the lines of the two main scenarios currently under discussion namely the logarithmic corrections scenario with critical exponents fixed in the ising universality class versus the weak universality scenario critical exponents varying with the degree of disorder is carried out in interpreting our data maximum care is constantly taken to be open to both possibilities a critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite size data s1063 651x 99 16110 5

picard groups in triangular geometry and applications to modular representation theory for a tensor triangulated p category k with spectrum spc k we construct an injective group homomorphism h 1 spc k m 1 p pic k 1 p where pic k is the group of invertible objects of k in modular representation theory we prove that this homomorphism induces a rational isomorphism between the picard group of the projective support variety and the group of endotrivial representations

criticality in the randomness induced second order phase transition of the triangular ising antiferromagnet with nearest and next nearest neighbor interactions abstract using a wang landau entropic sampling scheme we investigate the effects of quenched bond randomness on a particular case of a triangular ising model with nearest j n n and next nearest neighbor j n n n antiferromagnetic interactions we consider the case r j n n n j n n 1 for which the pure model is known to have a columnar ground state where rows of nearest neighbor spins up and down alternate and undergo a weak first order phase transition from the ordered to the paramagnetic state with the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first order phase transition to a second order phase transition and using the lee kosterlitz method we quantitatively verify this conversion the emerging under random bonds continuous transition shows a strongly saturating specific heat behavior corresponding to a negative exponent and belongs to a new distinctive universality class with 1 135 11 1 744 9 and 0 124 8 thus our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional 2d systems without and with quenched disorder

separability and triangulated categories abstract we prove that the category of modules over a separable ring object in a tensor triangulated category admits a unique structure of triangulated category which is compatible with the original one this applies in particular to etale algebras more generally we do this for exact separable monads

scaling analysis of the site diluted ising model in two dimensions a combination of recent numerical and theoretical advances are applied to analyze the scaling behavior of the site diluted ising model in two dimensions paying special attention to the implications for multiplicative logarithmic corrections the analysis focuses primarily on the odd sector of the model i e that associated with magnetic exponents and in particular on its lee yang zeros which are determined to high accuracy scaling relations are used to connect to the even thermal sector and a first analysis of the density of zeros yields information on the specific heat and its corrections the analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections

presheaves of triangulated categories and reconstruction of schemes to any triangulated category with tensor product k otimes we associate a topological space rm spc k otimes by means of thick subcategories of k a la hopkins neeman thomason moreover to each open subset u of this space spc k otimes we associate a triangulated category cal k u producing what could be thought of as a presheaf of triangulated categories applying this to the derived category k otimes rm d rm perf x otimes l of perfect complexes on a noetherian scheme x the topological space rm spc k otimes turns out to be the underlying topological space of x moreover for each open u subset x the category cal k u is naturally equivalent to rm d rm perf u as an application we give a method to reconstruct any reduced noetherian scheme x from its derived category of perfect complexes rm d rm perf x considering the latter as a tensor triangulated category with otimes l