eigenvalues for infinite matrices this paper is concerned with the problem of determining the location of eigenvalues for diagonally dominant infinite matrices upper and lower bounds for eigenvalues are established for tridiagonal matrices a numerical procedure for improving the bounds is given and the approximation of the eigenvectors is also discussed the techniques are illustrated for the solution of the well known mathieu s equation

eigenvalues of the laplacian in two dimensions the eigenvalue problem for the laplace operator in two dimensions is classical in mathematics and physics nevertheless computational methods for estimating the eigenvalues are still of much current interest particularly in applications to acoustic and electromagnetic waveguides although our primary interest is with the computational methods there are a number of theoretical results on the behavior of the eigenvalues and eigenfunctions that are useful for understanding the methods and in addition are of interest in themselves these results are discussed first and then the various computational methods that have been used to estimate the eigenvalues are reviewed with particular emphasis on methods that give error bounds some of the more powerful techniques available are illustrated by applying them to a model problem

a theory of algebraic cocycles we introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an eilenberg maclane space using these cocycles we develop a cohomology theory for complex algebraic varieties the theory is bigraded functorial and admits gysin maps it carries a natural cup product and a pairing to l homology chern classes of algebraic bundles are defined in the theory there is a natural transformation to singular integral cohomology theory that preserves cup products computations in special cases are carried out on a smooth variety it is proved that there are algebraic cocycles in each algebraic rational p p cohomology class in this announcement we present the outlines of a cohomology theory for algebraic varieties based on a new concept of an algebraic cocycle details will appear in fl our cohomology is a companion to the l homology theory recently studied in l f l f1 l f2 fm this homology is a bigraded theory based directly on the structure of the space of algebraic cycles it admits a natural transformation to integral homology that generalizes the usual map taking a cycle to its homology class our new cohomology theory is similarly bigraded and based on the structure of the space of algebraic cocycles it carries a ring structure coming from the complex join an elementary construction of projective geometry and it admits a natural transformation to integral cohomology chern classes are defined in the theory and transform under to the usual ones our definition of cohomology is very far from a duality construction on l homology nonetheless there is a natural and geometrically defined kronecker pairing between our morphic cohomology and l homology the foundation stone of our theory is the notion of an effective algebraic cocycle which is of some independent interest roughly speaking such a cocycle on a variety x with values in a projective variety y is a morphism from x to the space of cycles on y when x is normal this is equivalent by graphing to a cycle on x y with equidimensional fibres over x such cocycles abound in algebraic geometry and arise naturally in many circumstances the simplest perhaps is that of a flat morphism f x y whose corresponding cocycle associates to x x the pullback cycle f x many more arise naturally from synthetic constructions in projective geometry we show that every variety is rich in cocycles indeed if 1991 mathematics subject classification primary 14f99 14c05

an exact solution on the ferromagnetic face cubic spin model on a bethe lattice the lattice spin model with q component discrete spin variables restricted to have orientations orthogonal to the faces of q dimensional hypercube is considered on the bethe lattice the recursive graph which contains no cycles the partition function of the model with dipole dipole and quadrupole quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions the latter is calculated exactly in case of trees the system of two recurrent relations which allows to calculate all thermodynamic characteristics of the model is obtained the correspondence between thermodynamic phases and different types of fixed points of the rr is established using the technique of simple iterations the plots of the zero field magnetization and quadrupolar moment are obtained analyzing the regions of stability of different types of fixed points of the system of recurrent relations the phase diagrams of the model are plotted for q 2 the phase diagram of the model is found to have three tricritical points whereas for q 2 there are one triple and one tricritical points pacs number s 05 50 q 05 70 fh

exact spin spin correlation functions of bethe lattice ising and beg models in external fields we develop a transfer matrix method to compute exactly the spin spin correlation functions for bethe lattice ising model and blume emery griffiths beg model in the external magnetic field h and for any temperature t the correlation length t h obtained from the spin spin correlation function shows interesting scaling and divergent behavior as h 0 and t approaches the critical temperature tc

comparing k theories for complex varieties the semi topological k theory of a complex variety was defined in a recent paper by the authors with the expectation that it would prove to be a theory lying part way between the algebraic k theory of the variety and the topological k theory of the associated analytic space and thus would share properties with each of these other theories in this paper we realize these expectations by proving among other results that 1 the algebraic k theory with finite coefficients and the semi topological k theory with finite coefficients coincide on all projective complex varieties 2 semi topological k theory and topological k theory agree on certain types of generalized flag varieties and 3 assuming a result asserted by cohen and lima filho the semi topological k theory of any smooth projective variety becomes isomorphic to the topological k theory of the underlying analytic space once the bott element is inverted to illustrate the utility of our results we observe that a new proof of the quillen lichtenbaum conjecture for smooth complete curves is obtained as a corollary

eigenvalues of the laplacian on an elliptic domain the importance of eigenvalue problems concerning the laplacian is well documented in classical and modern literature finding the eigenvalues for various geometries of the domains has posed many challenges which include infinite systems of algebraic equations asymptotic methods integral equations etc in this paper we present a comprehensive account of the general solutions to helmholtz s equations defined on simply connected regions using complex variable techniques we consider boundaries of the form zz f z z or its inverse z z g zz to illustrate the theory we reduce the problem on elliptic domains to equivalent linear infinite algebraic systems where the coefficients of the infinite matrix are known polynomials of the eigenvalues we compute truncations of the infinite system for numerical values these values are compared to approximate values and some inequalities available in literature

approximately conserved quantity in the henon heiles problem a possible relation between an approximately conserved quantity in the h enon heiles problem and the integrals of the toda lattice is investigated a relation good to fifth order exactly and seventh order when averaged is proposed a form of averaging appears to be significant in the successful construction of approximately conserved quantities

mixed spin 12 and spin s ising ferrimagnets with a crystal field abstract the mixed spin 1 2 and spin s s 1 3 2 5 2 7 2 ising ferrimagnetic systems with a crystal field are studied within the framework of the exact recursion relations on the bethe lattice the phase diagrams and thermal behaviors of magnetizations are investigated numerically for the different values of lattice coordination numbers we find that the present system shows behaviors different from pure ising systems the results show that there is no compensation points for the system with half integer values

phase diagrams of the q state potts model on bethe lattices abstract we use a rigorous recently developed method of solution of spin models on bethe lattices cayley trees it allows us to detect all the phases of the ferromagnetic and antiferromagnetic q state potts models in a field fpm and apm respectively the phase diagrams of the fpm are characterized by three critical lines of first order transitions in the apm the ordered phases which appear always for h 0 and under certain conditions for h 0 and or h

global bethe lattice consideration of the spin 1 ising model the spin 1 ising model with bilinear and biquadratic exchange interactions and single ion crystal field is solved on the bethe lattice using exact recursion equations the general procedure of investigation of critical properties is discussed and a full set of phase diagrams are constructed for both positive and negative biquadratic couplings a comparison is made with the results of other approximation schemes

renormalisation groups with periodic and aperiodic orbits motivated by recent results for some frustrated hierarchical models the authors analyse the consequences of renormalisation group transformations with periodic and aperiodic orbits they find that the free energy has in general an infinite number of singularities this occurs already when the transformation has a stable periodic orbit they present an idealised example and a new class of hierarchical potts models to which the theory applies

analytical study of the superstable 3 cycle in the logistic map in the logistic map the simplest of stable odd numbered cycles is a 3 cycle it comes into existence after the stable 2k cycles cease to exist the 3 cycle is thus important as a route to chaos in 1977 guckenheimer et al j math biol 4 101 1977 first estimated the value of the control parameter a at which it can be superstable it implies that a stable 3 cycle can be formed and deformed at some values of a straddling that of the superstable 3 cycle in this work we present an exact value of a for the superstable 3 cycle by reducing a polynomial of degree 7 to that of 3 the relevance of this work to sharkovskii s theorem is also discussed

one dimensional mapping modulated phases and lyapunov exponent for the antiferromagnetic q state potts and multi site exchange interaction ising models abstract we describe the bifurcation structure period doubling and chaos for the antiferromagnetic q state potts model on the bethe lattice and three site interaction ising model on husimi one in a magnetic field by using the recursion relation technique a chaotic behavior of the magnetic susceptibility for the models is observed at low temperatures the resulting one dimensional rational mapping has a positive lyapunov exponent in the region of the chaotic regime for the antiferromagnetic q state potts q 2 and three site interaction ising models we discuss modulated phases for the antiferromagnetic q state potts q 2 and q 2 and three site interaction ising model at low temperatures the q state potts model q 2 has only one modulated phase with 1 2 pinching corresponding to the 2 cycle the q state potts q 2 and three site interaction ising models have an infinite number of modulated phases with different pinching numbers we construct the first modulated phase after the first bifurcation point

magnetic properties lyapunov exponent and superstability of the spin 12 ising heisenberg model on a diamond chain abstract the exactly solvable spin 1 2 ising heisenberg model on a diamond chain has been considered we have found the exact results for the magnetization using the recursion relation method the existence of the magnetization plateau has been observed at one third of the saturation magnetization in the antiferromagnetic case some ground state properties of the model are examined at low temperatures the system has two ferrimagnetic fri1 and fri2 phases and one paramagnetic prm phase lyapunov exponents for the various values of the exchange parameters and temperatures have been analyzed it has also been shown that the maximal lyapunov exponent exhibits plateau lyapunov exponents exhibit different behavior for two ferrimagnetic phases we have found the existence of the supercritical point for the multi dimensional rational mapping of the spin 1 2 ising heisenberg model on a diamond chain for the first time in the absence of the external magnetic field and t 0 in the antiferromagnetic case

levy statistics in a hamiltonian system enhanced diffusion in a hamiltonian system is studied in terms of the continuous time random walk formulation for l evy walks the previous l evy walk scheme is extended i to include interruptions by periods of temporal localization and ii to describe motion in two dimensions we analyze a case of conservative motion in a two dimensional periodic potential numerical calculations of the mean squared displacements and the propagators for intermediate energies are consistent with the l evy walk description

exact results of a general spin 1 model on 2d decorated lattices by the decoration iteration transformation we find a general relation between interaction parameters of a general spin 1 model on any lattice with unique coordination number and on its decorated lattice we obtain three exact phase transition points of the general spin 1 model on two dimensional decorated lattices in terms of the exact results of the model on corresponding two dimensional regular lattices including the triangle square kagome and honeycomb lattices we find the critical temperatures have no exact relation with the average coordination number and the type of coordination number for both the ising model and the general spin 1 model

topological hypercovers and 1 realizations we show that if u is a hypercover of a topological space x then the natural map hocolim u x is a weak equivalence this fact is used to construct topological realization functors for the 1 homotopy theory of schemes over real and complex fields in an appendix we also prove a theorem about computing homotopy colimits of spaces that are not cofibrant

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

partition function zeros and magnetization plateaus of the spin 1 ising heisenberg diamond chain abstract we study the properties of the generalized spin 1 ising heisenberg model on a diamond chain which can be considered as a theoretical model for the homometallic magnetic complex ni 3 c 4 h 2 o 4 2 3 oh 2 h 2 o 4 n 2 h 2 o n the model possesses a large variety of ground state phases due to the presence of biquadratic and single ion anisotropy parameters magnetization and quadrupole moment plateaus are observed at one and two thirds of the saturation value the distributions of yang lee and fisher zeros are studied numerically for a variety of values of the model parameters the usual value 1 2 alongside an unusual value 2 3 is determined for the yang lee edge singularity exponents

algebraic cycles on real varieties and z 2 equivariant homotopy theory in this paper the spaces of algebraic cycles on a real projective variety x are studied as z 2 spaces under the action of the galois group gal c r in particular the equivariant homotopy type of the group of algebraic p cycles zp pc is computed a version of lawson homology for real varieties is proposed the real lawson homology groups are computed for a class of real varieties

the gauge potts model on a generalized bethe lattice the q states gauge potts model is exactly solved on a special infinite dimensional lattice which is a bethe lattice of plaquettes the critical properties are studied the model exhibits a first order transition for any number of states q and coordination number gamma 1 the critical values of coupled constant beta c is shown to be in a good agreement with known results

fractal structure of zeros in hierarchical models we consider an ising and aq state potts model on a diamond hierarchical lattice we give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices ofq these zeros are just the julia set corresponding to the renormalization group transformation

backbone exponents of the two dimensional q state potts model a monte carlo investigation we determine the backbone exponent x b of several critical and tricritical q state potts models in two dimensions the critical systems include the bond percolation the ising the q 2 sqrt 3 3 and 4 state potts and the baxter wu model and the tricritical ones include the q 1 potts model and the blume capel model for this purpose we formulate several efficient monte carlo methods and sample the probability p2 of a pair of points connected via at least two independent paths finite size scaling analysis of p2 yields x b as 0 3566 2 0 2696 3 0 2105 3 and 0 127 4 for the critical q 2 sqrt 3 1 2 3 and 4 state potts model respectively at tricriticality we obtain x b 0 0520 3 and 0 0753 6 for the q 1 and 2 potts model respectively for the critical q 0 potts model it is derived that x b 3 4 from a scaling argument we find that at tricriticality x b reduces to the magnetic exponent as confirmed by the numerical results

dynamic phase diagrams of a ferrimagnetic mixed spin 1 2 1 ising system within the path probability method abstract in this study we used the path probability method ppm to calculate the dynamic phase diagrams of a ferrimagnetic mixed spin 1 2 1 ising system under an oscillating magnetic field one of the main advantages of the ppm over the mean field approximation and the effective field theory based on glauber type stochastic dynamics is that it contains two rate constants which are very important for studying dynamic behaviors we present the dynamic phase diagrams in the reduced magnetic field amplitude and reduced temperature plane and the twelve main different topological types of the phase diagrams are obtained the phase diagrams contain paramagnetic p ferrimagnetic i and i p mixed phases they also exhibit a dynamic tricritical and reentrant behavior as well as the dynamic double critical end point b critical end point e quadruple point qp and triple point tp the dynamic phase diagrams are compared and discussed with the phase diagrams obtained in previous works within the mean field approximation and the effective field theory based on glauber type stochastic dynamics

signs and approximate magnitudes of lyapunov exponents in continuous time dynamical systems methods for algebraically determining the signs and the magnitudes of lyapunov exponents of a given dynamical system are studied the existence of zero lyapunov exponents for the toda henon heiles and rossler systems are shown the approximate lyapunov spectra of lorenz and rossler systems are computed

a review of infinite matrices and their applications abstract infinite matrices the forerunner and a main constituent of many branches of classical mathematics infinite quadratic forms integral equations differential equations etc and of the modern operator theory is revisited to demonstrate its deep influence on the development of many branches of mathematics classical and modern replete with applications this review does not claim to be exhaustive but attempts to present research by the authors in a variety of applications these include the theory of infinite and related finite matrices such as sections or truncations and their relationship to the linear operator theory on separable and sequence spaces matrices considered here have special structures like diagonal dominance tridiagonal sign distributions etc and are frequently nonsingular moreover diagonally dominant finite and infinite matrices occur largely in numerical solutions of elliptic partial differential equations the main focus is the theoretical and computational aspects concerning infinite linear algebraic and differential systems using techniques like conformal mapping iterations truncations etc to derive estimates based solutions particular attention is paid to computable precise error estimates and explicit lower and upper bounds topics include bessel s mathieu equations viscous fluid flow simply and doubly connected regions digital dynamics eigenvalues of the laplacian etc also presented are results in generalized inverses and semi infinite linear programming

harnack thom theorem for higher cycle groups and picard varieties we generalize the harnack thom theorem to relate the ranks of the lawson homology groups with 22 coefficients of a real quasiprojective variety with the ranks of its reduced real lawson homology groups in the case of zero cycle group we recover the classical harnack thom theorem and generalize the classical version to include real quasiprojective varieties we use weil s construction of picard varieties to construct reduced real picard groups and milnor s construction of universal bundles to construct some weak models of classifying spaces of some cycle groups these weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors we obtain some congruences involving the picard number of a nonsingular real projective variety and the rank of its reduced real lawson homology groups of divisors

completions and fibrations for topological monoids we show that for a certain class of topological monoids there is a homotopy equivalence between the homotopy theoretic group completion m of a monoid m in that class and the topologized grothendieck group m associated to m the class under study is broad enough to include the chow monoids effective cycles associated to a projective algebraic variety and also the infinite symmetric products of finite cw complexes we associate principal fibrations to the completions of pairs of monoids showing the existence of long exact sequences for the naive approach to lawson homology fri91 lf91 a another proof of the eilenberg steenrod axioms for the functors x sp x in the category of finite cw complexes dold thom theorem dt56 is obtained

vanishing theorems for real algebraic cycles we establish the analogue of the friedlander mazur conjecture for teh s reduced lawson homology groups of real varieties which says that the reduced lawson homology of a real quasi projective variety x vanishes in homological degrees larger than the dimension of x in all weights as an application we obtain a vanishing of homotopy groups of the mod 2 topological groups of averaged cycles and a characterization in a range of indices of dos santos real lawson homology as the homotopy groups of the topological group of averaged cycles we also establish an equivariant poincare duality between equivariant friedlander walker real morphic cohomology and dos santos real lawson homology we use this together with an equivariant extension of the mod 2 beilinson lichtenbaum conjecture to compute some real lawson homology groups in terms of bredon cohomology

strange attractor in the ising model with competing interactions on the cayley tree on formule le modele d ising avec interactions de competition sur un arbre de cayley comme une application non lineaire a 2 dimensions

exact correlation functions of bethe lattice spin models in external magnetic fields we develop a transfer matrix method to compute exactly the spin spin correlation functions s 0 s n of bethe lattice spin models in the external magnetic field h and for any temperature t we first compute s 0 s n for the most general spin s ising model which contains all possible single ion and nearest neighbor pair interactions this general spin s ising model includes the spin frac 1 2 simple ising model and the blume emery griffiths beg model as special cases from the spin spin correlation functions we obtain functions of correlation length ensuremath xi t h for the simple ising model and beg model which show interesting scaling and divergent behavior as stackrel ensuremath rightarrow h 0 and t approaches the critical temperature t c our method to compute exact spin spin correlation functions may be applied to other ising type models on bethe and bethe like lattices

partition function zeros of the antiferromagnetic spin 1 2 ising heisenberg model on a diamond chain abstract the partition function zeros of the antiferromagnetic spin 1 2 ising heisenberg model on a diamond chain are studied using the transfer matrix method analytical equations for the distributions of yang lee and fisher zeros are derived the yang lee zeros are located on an arc of the unit circle and on the negative real axis in the complex magnetic fugacity plane in the limit t 0 the distribution pinches the positive real axis precipitating a phase transition fisher zeros manifest more complicated distributions depending on the values of the exchange parameters and external field densities of both categories of zeros are also studied the distributions of fisher zeros are investigated for different values of model parameters the yang lee and fisher edge singularity exponents are shown to be identical they are universal in nature and are calculated to be 1 2

visualization of special eigenmode shapes of a vibrating elliptical membrane analysis of eigenfunctions and eigenvalues of the laplacian is important in the understanding of distributed parameter vibration systems and quantum mechanics the elliptical domain is advantageous for such work because it allows the explicit representation of eigenfunctions as products of the mathieu functions in ann phys 9 1960 pp 24 75 kelley and rubinow used wave propagation geometrical optics and wkb methods to show that two special types of eigenmodes whispering gallery and bouncing ball modes exist on a general convex domain and they illustrated the case of an elliptical domain in this paper we develop a numerical package of the mathieu and modified mathieu functions to actually construct profiles of a sequence of eigenfunctions in order to visualize such special eigenmodes and others in the process we have also been able to observe a new type of transition state named focusing modes herein which seem to have a complementary behavior to the bouncing ball modes numerical eige

the spin 1 blume capel model with random crystal field on the bethe lattice abstract the dependence of the phase diagrams on the random crystal field rcf is investigated for the spin 1 blume capel bc model on the bethe lattice the calculations are carried out in terms of the recursion relations for the coordination number z 4 which corresponds to the square lattice the model presents tricritical points which are observed at lower negative crystal fields and higher temperatures for higher probabilities p and which vanish at lower p s the effect of randomness is illustrated for p 0 5 and shown that it changes the phase diagrams drastically from random to non random systems the reentrant behavior is also observed for appropriate p values

quaternionic algebraic cycles and reality in this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real brauer severi varieties under the action of the galois group gal c r appropriate stabilizations of these spaces yield two equivariant spectra the first one classifies dupont seymour s quaternionic k theory and the other one classifies an equivariant cohomology theory 3 which is a natural recipient of characteristic classes kh x 3 x for quaternionic bundles over real spaces x

complete analysis of ensemble inequivalence in the blume emery griffiths model we study inequivalence of canonical and microcanonical ensembles in the mean field blume emery griffiths model this generalizes previous results obtained for the blume capel model the phase diagram strongly depends on the value of the biquadratic exchange interaction k the additional feature present in the blume emery griffiths model at small values of k as for the blume capel model lines of first and second order phase transitions between a ferromagnetic and a paramagnetic phase are present separated by a tricritical point whose location is different in the two ensembles at higher values of k the phase diagram changes substantially with the appearance of a triple point in the canonical ensemble which does not find any correspondence in the microcanonical ensemble moreover one of the first order lines that starts from the triple point ends in a critical point whose position in the phase diagram is different in the two ensembles this line separates two paramagnetic phases characterized by a different value of the quadrupole moment these features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory finally we discuss ergodicity breaking which is highlighted by the presence of gaps in the accessible values of magnetization at low energies it also displays new interesting patterns that are not present in the blume capel model

order from disorder effect in the exactly solved mixed spin 1 2 1 ising model on fully frustrated triangles in triangles lattices abstract the mixed spin 1 2 1 ising model on two fully frustrated triangles in triangles lattices is exactly solved with the help of the generalized star triangle transformation which establishes a rigorous mapping correspondence with the equivalent spin 1 2 ising model on a triangular lattice it is shown that the mutual interplay between the spin frustration and single ion anisotropy gives rise to various spontaneously ordered and disordered ground states which differ mainly in an occurrence probability of the non magnetic spin state of the integer valued decorating spins we have convincingly evidenced a possible coexistence of the spontaneous long range order with a partial disorder within the striking ordered disordered ground state which manifests itself through a non trivial criticality at finite temperatures as well a rather rich critical behavior including the order from disorder effect and reentrant phase transitions with either two or three successive critical points is also found

galois equivariance and stable motivic homotopy theory for a finite galois extension of fields l k with galois group g we study a functor from the g equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical galois correspondence we show that after completing at a prime and the motivic hopf map this results in a full and faithful embedding whenever k is real closed and l k i it is a full and faithful embedding after completion if a motivic version of serre s finiteness theorem is valid we produce strong necessary conditions on the field extension l k for this functor to be full and faithful along the way we produce several results on the stable c2 equivariant betti realization functor and prove convergence theorems for the p primary c2 equivariant adams spectral sequence

equations of motion approach to the spin 1 2 ising model on the bethe lattice we exactly solve the ferromagnetic spin 1 2 ising model on the bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the green s function formalism in particular such an approach is applied to an isomorphic model of localized fermi particles interacting via an intersite coulomb interaction a complete set of eigenoperators is found together with the corresponding eigenvalues the green s functions and the correlation functions are written in terms of a finite set of parameters to be self consistently determined a procedure is developed that allows us to exactly fix the unknown parameters in the case of a bethe lattice with any coordination number z nonlocal correlation functions up to four points are also provided together with a study of the relevant thermodynamic quantities

phase diagrams and tricritical effects in the beg model abstract the critical properties of the spin 1 ising model on the bethe lattice with dipolar and quadrupolar exchange interactions are studied exactly this method is based on recursion relations which are exact in the infinite dimensional case and as a result the phase diagrams are constructed the line ending in the tricritical point is defined exactly it is shown that when the quadrupolar exchange interaction is large enough the tricritical point disappears the tricritical exponents are calculated exactly

generalized transformation for decorated spin models abstract the paper discusses the transformation of decorated ising models into an effective undecorated spin model using the most general hamiltonian for interacting ising models including a long range and high order interactions the inverse of a vandermonde matrix with equidistant nodes s s is used to obtain an analytical expression of the transformation this kind of transformation is very useful to obtain the partition function of decorated systems the method presented by fisher is also extended in order to obtain the correlation functions of the decorated ising models transforming into an effective undecorated ising model we apply this transformation to a particular mixed spin 1 2 1 and 1 2 2 square lattice with only nearest site interaction this model could be transformed into an effective uniform spin s square lattice with nearest and next nearest interaction furthermore the effective hamiltonian also includes combinations of three body and four body interactions in particular we considered spin 1 and 2

spin 1 blume capel model with random crystal field effects abstract the random crystal field spin 1 blume capel model is investigated by the lowest approximation of the cluster variation method which is identical to the mean field approximation the crystal field is either turned on randomly with probability p or turned off with q 1 p in a bimodal distribution then the phase diagrams are constructed on the crystal field temperature k t j planes for given values of p and on the k t j p planes for given by studying the thermal variations of the order parameters in the latter we only present the second order phase transition lines because of the existence of irregular wiggly phase transitions which are not good enough to construct lines in addition to these phase transitions the model also yields tricritical points for all values of p and the reentrant behavior at lower p values

rational isomorphisms between k theories and cohomology theories the well known isomorphism relating the rational algebraic k theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map the segre map of infinite loop spaces moreover the associated chern character map on rational homotopy groups is shown to be a ring isomorphism a technique is introduced that establishes a useful general criterion for a natural transformation of functors on quasi projective complex varieties to induce a homotopy equivalence of semi topological singular complexes since semi topological k theory and morphic cohomology can be formulated as the semi topological singular complexes associated to algebraic k theory and motivic cohomology this criterion provides a rational isomorphism between the semi topological k theory groups and the morphic cohomology groups of a smooth complex variety consequences include a riemann roch theorem for the chern character on semi topological k theory and an interpretation of the topological filtration on singular cohomology groups in k theoretic terms

reentrant phase transitions and multicompensation points in the mixed spin ising ferrimagnet on a decorated bethe lattice abstract a mixed spin ising model on a decorated bethe lattice is rigorously solved by combining the decoration iteration transformation with the method of exact recursion relations exact results for critical lines compensation temperatures total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin 1 2 ising model on a simple undecorated bethe lattice the effect of next nearest neighbour interaction and single ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular it is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs the single ion anisotropy dependence basically changes with the coordination number of the underlying bethe lattice the possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying bethe lattice

mixed spin 2 and spin 5 2 blume emery griffiths model abstract the mixed spin 2 and spin 5 2 blume emery griffiths beg ising ferrimagnetic system is studied on the bethe lattice using the exact recursion equations with the coordination number q 3 corresponding to the honeycomb lattice on real lattices the influences of the crystal field and the biquadratic interactions are investigated by obtaining the phase diagrams on the k j kt j and d j kt j planes respectively with equal crystal field interactions for the sublattices the model presents very rich critical behaviors which includes the first and second order phase transitions thus also the tricritical and critical end points are observed we have also found that the model gives up to four compensation temperatures for appropriate values of the system parameters

blume emery griffiths model on the honeycomb lattice exact results are obtained for a spin 1 system on the honeycomb lattice with the blume emery griffiths hamiltonian kt j i jsisj k i j si2j2 isi2 h si subject to the constraintk ln coshj forj 0 the system behaves like a spin 1 2 ising ferromagnet with the free energy analytic everywhere except at the first order phase boundaryh 0 tanhj 2 e sqrt 3 derivatives of the free energy across this boundary are discontinuous and we obtain the exact expression for the spontaneous magnetization forj 0 the system can be transcribed into an antiferromagnetic spin 1 2 ising model in a real magnetic field and from this equivalence portions of the exact phase boundary are determined

chaotic dynamics and superdiffusion in a hamiltonian system with many degrees of freedom abstract we discuss recent results obtained for the hamiltonian mean field model the model describes a system of n fully coupled particles in one dimension and shows a second order phase transition from a clustered phase to a homogeneous one when the energy is increased strong chaos is found in correspondence to the critical point on top of a weak chaotic regime which characterizes the motion at low energies for a small region around the critical point we find anomalous enhanced diffusion and levy walks in a transient temporal regime before the system relaxes to equilibrium