conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

discrete mass spectrum of z n spin systems perturbed by a thermal field the author calculates numerically the lowest masses in the discrete mass spectrum of the z n fateev zamolodchikov spin model 1985 perturbed by a thermal operator the mass ratios obtained are in agreement with those derived from the s matrix introduced by koberle and swieca 1979

character degree graphs and normal subgroups we consider the degrees of those irreducible characters of a group g whose kernels do not contain a given normal subgroup n we show that if n g and n is not perfect then the common divisor graph on this set of integers has at most two connected components also if n is solvable we obtain bounds on the diameters of the components of this graph and in the disconnected case we study the structure of n and of g

semiprojectivity and properly infinite projections in graph c algebras abstract we give a complete description of which unital graph c algebras are semiprojective and use it to disprove two conjectures by blackadar to do so we perform a detailed analysis of which projections are properly infinite in such c algebras

on the phase diagram of the discrete z6 spin models we point out some problems with the previously proposed phase diagram of the z6 spin models consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies with the aid of a new parametrization of the phase space we study the models numerically with results which support our conjectures

identifying af algebras that are graph c algebras abstract we consider the problem of identifying exactly which af algebras are isomorphic to a graph c algebra we prove that any separable unital type i c algebra with finitely many ideals is isomorphic to a graph c algebra this result allows us to prove that a unital af algebra is isomorphic to a graph c algebra if and only if it is a type i c algebra with finitely many ideals we also consider nonunital af algebras that have a largest ideal with the property that the quotient by this ideal is the only unital quotient of the af algebra we show that such an af algebra is isomorphic to a graph c algebra if and only if its unital quotient is type i which occurs if and only if its unital quotient is isomorphic to m k for some natural number k all of these results provide vast supporting evidence for the conjecture that an af algebra is isomorphic to a graph c algebra if and only if each unital quotient of the af algebra is type i with finitely many ideals and bear relevance for the extension problem for graph c algebras

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

parafermions and surface exponents of self dual z n spin models from conformal invariance the author studies the critical behaviour of a family of self dual two dimensional spin models with z n symmetry n or 8 in its hamiltonian formulation using the relations between the mass gap amplitudes of the hamiltonian in a finite strip and the critical exponents he estimates the anomalous dimensions of the parafermions occurring in the underlying field theory as well as the surface exponents

the ashkin teller quantum chain and conformal invariance the authors study the finite size effects for the fourth state one dimensional quantum chain introduced by kohmoto et al 1981 using different boundary conditions from the corrections to the ground state energy for periodic boundary conditions they verify that the central charge of the virasoro algebra is equal to one in the whole domain of criticality their numerical study suggests a new relation between the corrections to the ground state energy with free boundary conditions and with periodic boundary conditions various critical exponents including the surface ones and those corresponding to the para fermions are determined

finite lattice extrapolations for z3 and zs models a method is presented to accelerate the convergence of finite lattice sequences to their bulk limit the calculation of highly accurate estimates of the critical parameters of the bulk system is then possible applied to the hamiltonian version of the z3 model three state potts model in 1 1 dimensions these techniques yield estimates for the exponents gamma 1 444 or 0 0001 nu 0 8333 or 0 0003 and alpha 0 33 or 0 01 for the z5 model the presence of a kosterlitz thouless transition is confirmed

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

period two automorphisms of uhf c algebras recently 7 fack and marechal classified the product symmetries of a uhf c algebra among these product symmetries there is a distinguished element si whose fixed point algebra is uhf since they dealt with product symmetries all fixed point algebras are automatically af the symmetry s is characterized among product symmetries by the property pm this had been noted earlier by kishimoto 151

phase diagram in the generalized chiral clock models abstract using the results of the integrable chiral potts model we speculate about the possible phase diagram of the generalized chiral clock model in the integrable model it is found that the chiral fields are almost proportional to one another here we consider a chiral model with all the chiral fields exactly proportional to one another with fixed proportionality constants given by the integrable case this reduces the chiral field variables to just one denoted by the model thus defined includes the generalized clock model or z n model at 0 or 1 2 and the chiral clock models as special cases using the results of many authors on the z n model in the so called symmetric case with vertical and horizontal interactions equal and the behavior of the system at t 0 we can get a pretty good picture of the phase diagram of this chiral model the exact results show that the commonly held belief that the massless phase in the z n model for n 5 is in the same universality class as the classical xy model and the belief that the commensurate incommensurate phase transition is of the pokrovskii talapov type and the incommensurate fluid transition is of kosterlitz thouless type may not be correct as universality may not even hold on these phase boundaries

unusual universality of branching interfaces in random media we study the criticality of a potts interface by introducing a froth model which unlike its solid on solid ising counterpart incorporates bubbles of different phases the interface is fractal at the phase transition of a pure system however a position space approximation suggests that the probability of loop formation vanishes marginally at a transition dominated by strong random bond disorder this implies a linear critical interface and provides a mechanism for the conjectured equivalence of critical random potts and ising models

bounding fitting heights of character degree graphs ofg written g isthegraphwhosevertexsetis g twoverticespandqin g areadjacentifthereis some degree a cd g where pqdivides a these graphs have beenstudiedinseveralplaces thebestsourcesforgeneralinformationaboutthese graphs are theorem 14 of 2 chapter 30 of 3 and sections 18and19of 10 in 8 adegreegraph wassaidtohave

spectral analysis for automorphisms of uhf c algebras abstract we study outer conjugacy for aperiodic automorphisms of uhf c algebras we show the existence of an action on the universal uhf algebra which is absorbing via tensor product for product actions we provide an explicit criterion for the action to be absorbing this criterion involves the eventual uniform distribution mod 1 of the eigenvalues of the approximating unitaries

critical behavior of the random bond ashkin teller model a monte carlo study the critical behaviour of a bond disordered ashkin teller model on a square lattice is investigated by intensive monte carlo simulations a duality transformation is used to locate a critical plane of the disordered model this critical plane corresponds to the line of critical points of the pure model along which critical exponents vary continuously along this line the scaling exponent corresponding to randomness varies continuously and is positive so that randomness is relevant and different critical behaviour is expected for the disordered model we use a cluster algorithm for the monte carlo simulations based on the wolff embedding idea and perform a finite size scaling study of several critical models extrapolating between the critical bond disordered ising and bond disordered four state potts models the critical behaviour of the disordered model is compared with the critical behaviour of an anisotropic ashkin teller model which is used as a refference pure model we find no essential change in the order parameters critical exponents with respect to those of the pure model the divergence of the specific heat c is changed dramatically our results favor a logarithmic type divergence at tc c logl for the random bond ashkin teller and four state potts models and c log logl for the random bond ising model

multi particle structure in the zn chiral potts models the authors calculate the lowest translationally invariant levels of the z3 and z4 symmetrical chiral potts quantum chains using numerical diagonalization of the hamiltonian for n or 12 and n or 10 sites respectively and extrapolating n to infinity in the high temperature massive phase they find that the pattern of the low lying zero momentum levels can be explained assuming the existence of n 1 particles carrying zn charges q 1 n 1 mass mq and their scattering states in the superintegrable case the masses of the n 1 particles become proportional to their respective charges mq qm1 exponential convergence in n is observed for the single particle gaps while power convergence is seen for the scattering levels they also verify that qualitatively the same pattern appears for the self dual and integrable cases for general zn they show that the energy momentum relations of the particles show a parity nonconservation asymmetry which for very high temperatures is exclusive due to the presence of a macroscopic momentum pm 1 2q n phi where phi is the chiral angle and q is the zn charge of the respective particle

a monte carlo renormalisation group study of the two dimensional discrete cubic model a hint for superconformal invariance the discrete cubic model for six states of the lattice variables is investigated at one special point of the phase diagram where a number of contradicting results are known concerning the order of the phase transition and the critical exponents a new implementation of the mcrg method is used for determining the critical point with great accuracy and for calculating the critical exponents a continuous phase transition is found following the recent results for six state self dual quantum chains with cubic symmetry where for a special point superconformal invariance is discovered the critical exponents obtained are explained in the framework of this theory indicating a superconformal point with a conformal anomaly of c 1 25

an answer to a question of isaacs on character degree graphs abstract let n be a normal subgroup of a finite group g we consider the graph g n whose vertices are the prime divisors of the degrees of the irreducible characters of g whose kernel does not contain n and two vertices are joined by an edge if the product of the two primes divides the degree of some of the characters of g whose kernel does not contain n we prove that if g n is disconnected then g n is solvable this proves a strong form of a conjecture of isaacs

a simple separable exact c algebra not anti isomorphic to itself we give an example of an exact stably finite simple separable c algebra d which is not isomorphic to its opposite algebra moreover d has the following additional properties it is stably finite approximately divisible has real rank zero and stable rank one has a unique tracial state and the order on projections over d is determined by traces it also absorbs the jiang su algebra z and in fact absorbs the 3 uhf algebra we can also explicitly compute the k theory of d namely k 0 d cong mathbb z tfrac 1 3 with the standard order and k1 d 0 as well as the cuntz semigroup of d namely w d cong mathbb z tfrac 1 3 sqcup 0 infty

finite lattice methods in quantum hamiltonian field theory i o 2 and o 3 heisenberg models for pt i see ibid vol 14 p 241 57 1981 two efficient methods for finding the low lying states of hamiltonians on finite lattices are described the first involves constructing a finite representation of the hamiltonian using strong coupling eigenstates while the second is based on the lanczos recursion method the methods are used to determine the mass gap of the o 2 and o 3 heisenberg hamiltonians in 1 1 dimensions for a sequence of finite chains the critical behaviour of the infinite chain is then analysed by extrapolating the finite lattice estimates using finite size scaling a remarkably sensitive test is developed for the presence of a phase transition for the o 2 model data this test yields strong evidence for a phase transition with the weak coupling phase massless while in the o 3 case the test supports although more weakly the absence of any transition

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

finite group actions on c algebras with the rohlin property i basic properties of finite group actions with the rohlin property on unital c algebras are investigated a characterization of finite group actions with the rohlin property on the cuntz algebra 02 is given in terms of central sequences which may be considered as an equivariant version of e kirchberg and n c phillips s characterization of 02 a large class of symmetries on 02 are classified in terms of the fixed point algebras for conjugacy and the crossed products for cocycle conjugacy model actions of symmetries of 02 are constructed for given k theoretical invariants

the spin s xxz quantum chain with general toroidal boundary conditions the authors derive the operator content of the spin s xxz quantum chain with generalised toroidal boundary conditions compatible with the u 1 symmetry of the model these results are derived by solving numerically the associated bethe ansatz equations for finite chains and exploring the consequences of the conformal invariance of the infinite system they also show that as in the spin 1 2 case the conformal anomaly and dimensions of general extended su 2 algebras can be obtained from these spin s chains by choosing properly the coupling constant and the boundary condition

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

conformal invariance and the critical behaviour of a quantum spin hamiltonian with three spin coupling a quantum spin model with three spin coupling is studied by finite lattice methods the critical indices nu and alpha are obtained by standard finite size scaling analysis conformal invariance is used to estimate the exponents nu and eta the central charge or conformal anomaly c and the anomalous dimension of a spin 1 4 parafermion the authors conclude that the model belongs to the same universality class as the four state potts and baxter wu models although the convergence of the various finite lattice estimators is extremely slow

bounding graph diameters of nonsolvable groups abstract associated with the character degrees of a finite group is the common divisor graph where the nontrivial degrees are the vertices and distinct degrees are adjacent when they have a common nontrivial divisor the author has shown that common divisor graphs for solvable groups have diameters of at most 3 the present paper extends this result to nonsolvable groups by showing that their common divisor graphs also have diameters bounded above by 3

z 6 model criticality and break collapse method abstract the phase diagram and thermal and crossover exponents of the z 6 ferromagnet on the square lattice are calculated within a real space renormalization group rg scheme the obtained phase diagram exhibiting 4 phases corresponding to z 6 z 3 z 2 and completely broken symmetries contains all exactly known critical points and possibly is an excellent approximation everywhere except in the high temperature region where a soft phase is expected to appear however all the obtained results are exact in the wheatstone bridge hierarchical lattice in addition to these results we present an operational procedure the break collapse method which considerably simplifies the exact calculation of two spin correlation functions for arbitrary z 6 two rooted clusters frequent in rg approaches

equivariant homomorphisms rokhlin constraints and equivariant uhf absorption abstract we classify equivariant homomorphisms between c dynamical systems associated to actions of finite groups with the rokhlin property in addition the given actions are classified an obstruction is obtained for the cuntz semigroup of a c algebra allowing such an action we also obtain an equivariant uhf absorption result

transitive actions of locally compact groups on locally contractible spaces suppose that xdg k is the quotient of a locally compact group by a closed subgroup ifx is locally contractible and connected we prove thatx is a manifold if theg action is faithful theng is a lie group

applications of model theory to c dynamics we initiate the study of compact group actions on c algebras from the perspective of model theory and present several applications to c dynamics firstly we prove that the continuous part of the central sequence algebra of a strongly self absorbing action is indistinguishable from the continuous part of the sequence algebra and in fact equivariantly isomorphic under the continuum hypothesis as another application we present a unified approach to several dimensional inequalities in c algebras which is done through the notion of order zero dimension for an equivariant homomorphism finiteness of the order zero dimension implies that the dimension of the target algebra can be bounded by the dimension of the domain the dimension can be among others decomposition rank nuclear dimension or rokhlin dimension as a consequence we obtain new inequalities for these quantities as a third application we obtain the following result if a c algebra a absorbs a strongly self absorbing c algebra d and is an action of a compact group g on a with finite rokhlin dimension with commuting towers then absorbs any strongly self absorbing action of g on d this has a number of interesting consequences already in the case of the trivial action on d for example we deduce that d stability passes from a to the crossed product additionally in many cases of interest our result restricts the possible values of the rokhlin dimension to and showing a striking parallel to the behavior of the nuclear dimension for simple c algebras we also show that an action of a finite group with finite rokhlin dimension with commuting towers automatically has the rokhlin property if the algebra is uhf absorbing

the bond diluted z q ferromagnetic model criticality and break collapse method within a real space renormalization group rg which preserves two site correlation functions we study on the square lattice the criticality of the bond diluted z q ferromagnetic model we generalize the break collapse method which simplifies greatly the exact calculation of arbitrary z q two terminal clusters commonly appearing in rg approaches mainly for a large value of q we reproduce in the pure case several known exact results the structure of the phase diagrams for all the values of q is obtained with a good precision the massless spin wave like phase which evolves into the kosterlitz touless phase for occurs around in agreement with the well known exact result the structure of the phase diagrams in the diluted case is qualitatively similar to that obtained from the pure model the massless spin wave like phase resists in an interval of concentration p which increases for the large values of q

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

localization in a simple multichain catalytic absorption model we consider the phase transition in the ensemble of n polymer chains developing on the halfline all chains are independent of each other in all points except the origin x 1 where the point well is located the well depth depends on the number of beads of different chains simultaneously staying at the point x 1 we show that if the well depth grows faster than with n then all chains become localized simultaneously at the origin in the limit in the conclusion we discuss the connection of the above defined problem with the phase transition in the copolymer chain with a quenched random sequence of monomers using the replica approach

the critical behaviour of self dual z n spin systems finite size scaling and conformal invariance this paper is concerned with the critical properties of a family of self dual two dimensional z n models whose bulk free energy is exactly known at the self dual point the author s analysis is performed by studying the finite size behaviour of the corresponding one dimensional quantum hamiltonians which also possess an exact solution at their self dual point by exploring finite size scaling ideas and the conformal invariance of the critical infinite system the author calculates for n up to 8 the critical temperature and critical exponents as well as the central charge associated with the underlying conformal algebra the results strongly suggest that the z n quantum field theory of zamolodchikov and fateev is the underlying field theory associated with these statistical mechanical systems the author also tests for the z 5 case the conjecture that these models correspond to the bifurcation points in the phase diagram of the general z n spin model where a massless phase originates

a class of c algebras generalizing both graph algebras and homeomorphism c algebras i fundamental results we introduce a new class of c algebras which is a generalization of both graph algebras and homeomorphism c algebras this class is very large and also very tractable we prove the so called gauge invariant unique ness theorem and the cuntz krieger uniqueness theorem and compute the k groups of our algebras

finite size scaling and conformal invariance in a self dual quantum z 5 model considers the critical behaviour of a particular set of onedimensional self dual models with z n symmetry n or 5 the critical indices are evaluated using standard finite size scaling and by exploiting their relations with the mass gap amplitudes predicted by conformal invariance the results strongly suggest that the recently introduced z n quantum field theory is the underlying field theory for these statistical mechanics models

q state potts models in hamiltonian field theory for q 4 in 1 1 dimensions finite lattice sequence extrapolation methods are applied to the q state potts models in 1 1 d hamiltonian field theory thermal exponents nu 0 71 or 0 02 alpha 0 53 or 0 02 are obtained for the four state model methods are discussed for treating the first order transitions for q 4 and a sequence extrapolation is used to estimate the latent heat exact analytic formulae are derived for the ground state energy the mass gap and the latent heat at the transition point these are compared with the numerical results

the correlation length of the potts model at the first order transition point the authors consider the q state two dimensional potts model for q g i e in the first order phase transition regime following a scheme given by p martin 1991 the authors prove an identity between the spectra of the transfer matrices of the potts model and the transfer matrices connecting the diagonals of a 6 vertex model by using a bethe ansatz for the latter they obtain an exact expression for the correlation length of the potts model at the transition point

hunting for the central charge of the virasoro algebra six and eight state spin models in two dimensions conformal invariance has important implications for the finite size scaling properties of the spectra of transfer matrices and quantum chains at the critical point some relations between the finite size scaling amplitudes are obtained which can be used as a test of conformal invariance and implicitly to distinguished between second order and first order phase transitions the numerical values of the scaling amplitudes give the scale dimensions of various operators six and eight state self dual quantum chains with cubic symmetries are considered at the critical point for three values of the coupling constant the systems are found to be conformal invariant and estimates for several critical exponents are obtained based on the approximate values of the critical exponent one tries to find the values of the corresponding central charges of the virasoro algebras

crossed products by finite group actions with the rokhlin property we prove that a number of classes of separable unital c algebras are closed under crossed products by finite group actions with the rokhlin property including a ai algebras at algebras and related classes characterized by direct limit decompositions using semiprojective building blocks b simple unital ah algebras with slow dimension growth and real rank zero c c algebras with real rank zero or stable rank one d simple c algebras for which the order on projections is determined by traces e c algebras whose quotients all satisfy the universal coefficient theorem f c algebras with a unique tracial state along the way we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective

the tracial rokhlin property for actions of finite groups on c algebras we define tracial analogs of the rokhlin property for actions of finite groups approximate representability of actions of finite abelian groups and approximate innerness we prove the following four analogs of related nontracial results bullet the crossed product of an infinite dimensional simple separable unital c algebra with tracial rank zero by an action of a finite group with the tracial rokhlin property again has tracial rank zero bullet an outer action of a finite abelian group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property if and only if its dual is tracially approximately representable and is tracially approximately representable if and only if its dual has the tracial rokhlin property bullet if a strongly tracially approximately inner action of a finite cyclic group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property then it is tracially approximately representable bullet an automorphism of an infinite dimensional simple separable unital c algebra a with tracial rank zero is tracially approximately inner if and only if it is the identity on k 0 a mod infinitesimals

actions of rigid groups on uhf algebras let be a countably infinite property t group and let d be uhf algebra of infinite type we prove that there exists a continuum of pairwise non weakly cocycle conjugate strongly outer actions of on d the proof consists in assigning to any second countable abelian pro p group g a strongly outer action of on d whose weak cocycle conjugacy class completely remembers the group g the group g is reconstructed from the action through its weak 1 cohomology set endowed with a canonical pairing function our construction also shows the following stronger statement the relations of conjugacy cocycle conjugacy and weak cocycle conjugacy of strongly outer actions of on d are complete analytic sets and in particular not borel the same conclusions hold more generally when is only assumed to contain an infinite subgroup with relative property t and for actions on not necessarily simple separable nuclear uhf absorbing self absorbing c algebras with at least one trace finally we use the techniques of this paper to construct outer actions on r with prescribed cohomology precisely for every infinite property t group and for every countable abelian group we construct an outer action of on r whose 1 cohomology is isomorphic to

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

finite size studies of the ashkin teller model the authors study the ashkin teller model in the time continuous hamiltonian version finite size scaling is used to calculate the magnetic gamma m electric gamma p and thermal alpha and nu critical exponents for several values of the coupling constant lambda the results confirm the believed extended scaling relations and suggest a conjecture relating the mass gap amplitudes and critical indices in the hamiltonian context

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we study the dynamic critical behavior of a swendsen wang type algorithm for the ashkin teller model we find that the li sokal bound on the autocorrelation time int const xc h holds along the self dual curve of the symmetric ashkin teller model and is almost but not quite sharp the ratio int c h appears to tend to infinity either as a logarithm or as a small power 0 05 p 0 12 in an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time

finite group actions on c algebras with the rohlin property ii abstract we classify finite group actions on some classes of c algebras with the rohlin property in terms of the k groups a group cohomological obstruction is obtained for the k groups of a c algebra allowing such an action for example the tate cohomology groups with the k groups as the coefficient modules must vanish model actions with the rohlin property are constructed for given k theoretical invariants quasi free actions of finite cyclic groups on the cuntz algebras and their dual actions are investigated from the view point of the rohlin property

semiprojectivity with and without a group action abstract the equivariant version of semiprojectivity was recently introduced by the first named author we study properties of this notion in particular its relation to ordinary semiprojectivity of the crossed product and of the algebra itself we show that equivariant semiprojectivity is preserved when the action is restricted to a cocompact subgroup thus if a second countable compact group acts semiprojectively on a c algebra a then a must be semiprojective this fails for noncompact groups we construct a semiprojective action of z on a nonsemiprojective c algebra we also study equivariant projectivity and obtain analogous results however with fewer restrictions on the subgroup for example if a discrete group acts projectively on a c algebra a then a must be projective this is in contrast to the semiprojective case we show that the crossed product by a semiprojective action of a finite group on a unital c algebra is a semiprojective c algebra we give examples to show that this does not generalize to all compact groups

renormalisation group study of a disordered model we study the potts model on a diamond hierarchical lattice with random interactions using weak disorder expansions we calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent ap of the pure system becomes positive at ap 0 we find how the logarithmic singularity is modified by the disorder lastly we suggest that this model should present griffiths like singularities

semiprojectivity for certain purely infinite c algebras it is proved that classifiable simple separable nuclear purely infinite c algebras having finitely generated k theory and torsion free k 1 are semiprojective this is accomplished by exhibiting these algebras as c algebras of infinite directed graphs