classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

bounded perturbations of the generalized random fields functional dlr equations corresponding to the bounded perturbations of sufficiently regular generalized gaussian random fields are studied certain uniqueness theorems are proved some qualitative properties of the set of the corresponding gibbs states are described

entropy and global markov properties we extend refine and give simple proofs of some recent results on the validity of global markov properties for classical spin systems one of the new results is that there is a global markov property that is satisfied by equilibrium states in general the proof of this establishes formulas for the entropy and free energy that show that these quantities are ford dimensional systems given in terms of d 1 dimensional systems furthermore we show that global markov properties imply the absence of some types of symmetry breaking

splitting in large dimension and infrared estimates ii moment inequalities this is the continuation of notes written for the nato asi conference in il ciocco september 96 consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the schrodinger operator h and the proof of infrared estimates for quantities attached to gaussian type measures these notes were mainly reporting on the old contributions of dyson frohlich glimm jaffe lieb simon and spencer in the 1970s in connection with more recent contributions of pastur khoruzhenko barbulyak and kondrat ev which treat in general more sophisticated models here we concentrate on the simplest model related to field theory and extend the results of barbulyak and kondrat ev by mixing ideas coming from pastur and khozurenko related to the use of bogolyubov s inequality with classical inequalities due to ginibre lebowitz sokal and others or in the case when the temperature t is zero by applying rather elementary estimates on schrodinger operators in order to find

euclidean gibbs measures on loop lattices existence and a priori estimates we present a new method to prove existence and uniform a priori estimates for euclidean gibbs measures corresponding to quantum anharmonic crystals it is based first on the alternative characterization of gibbs measures in terms of their logarithmic derivatives through integration by parts formulas and second on the choice of appropriate lyapunov functionals

uniqueness and global markov property for euclidean fields the case of general polynomial interactions we give a general method for proving uniqueness and global markov property for euclidean quantum fields the method is based on uniform continuity of local specifications proved by using potential theoretical tools and exploitation of a suitable fkg order structure we apply this method to give a proof of uniqueness and global markov property for the gibbs states and to study extremality of gibbs states also in the case of non uniqueness in particular we prove extremality for 2 4 also in the case of non uniqueness and global markov property for weak coupling 2 4 which solves a long standing problem uniqueness and extremality holds also at any point of differentiability of the pressure with respect to the external magnetic field

proposed experimental tests of the bell kochen specker theorem for a two particle two state system sets of compatible propositions exist for which quantum mechanics and noncontextual hidden variable theories make conflicting predictions for every individual system whatever its quantum state this permits a simple all or nothing state independent experimental verification of the bell kochen specker theorem

the repulsive lattice gas the independent set polynomial and the lovasz local lemma we elucidate the close connection between the repulsive lattice gas in equi librium statistical mechanics and the lovasz local lemma in probabilistic com binatorics we show that the conclusion of the lovasz local lemma holds for dependency graph g and probabilities px if and only if the independent set polynomial for g is nonvanishing in the polydisc of radii px furthermore we show that the usual proof of the lovasz local lemma which provides a suffi cient condition for this to occur corresponds to a simple inductive argument for the nonvanishing of the independent set polynomial in a polydisc which was discovered implicitly by shearer 98 and explicitly by dobrushin 37 38 we also present some refinements and extensions of both arguments including a generalization of the lovasz local lemma that allows for soft dependencies in addition we prove some general properties of the partition function of a repulsive lattice gas most of which are consequences of the alternating sign property for the mayer coefficients we conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs

fractal haar system abstract the haar system is an alternative to the classical fourier bases being particularly useful for the approximation of discontinuities the article tackles the construction of a set of fractal functions close to the haar set the new system holds the property of constitution of bases of the lebesgue spaces of p integrable functions on compact intervals likewise the associated fractal series of a continuous function is uniformly convergent the case p 2 owns some peculiarities and is studied separately

modified runge kutta methods for the numerical solution of odes with oscillating solutions three new modified runge kutta methods with minimal phase lag are developed for the numerical solution of ordinary differential equations with oscillating solutions these methods are based on the well known runge kutta method of dormand and prince rk5 4 t see 1 of order five numerical and theoretical results show that this new approach is more efficient compared with the well known classical fifth order runge kutta dormand and prince method

application of log sobolov inequality to the stochastic dynamics of unbounded spin systems on the lattice abstract we consider a ferromagnetic lattice spin system with unbounded spins and investigate the relaxation property for the associated stochastic dynamics the glauber dynamics in the finite volume case we prove that the following two conditions are equivalent 1 the log sobolev inequality for the finite volume gibbs states holds uniformly in both the volume and the boundary condition 2 the finite volume glauber dynamics relaxes to equilibrium exponentially fast uniformly in the volume whenever it starts from a tempered configuration this can be considered as a complementary result to the ones previously obtained for infinite volume glauber dynamics by b zegarlinski 1996 comm math phys 175 401 432 our result can also be viewed as an extension of the equivalence theorem known for compact spin space settings

ergodicity ofl2 semigroups and extremality of gibbs states we extend the classical results of holley stroock on the characterization of extreme gibbs states for the ising model in terms of the irreducibility resp ergodicity of the corresponding glauber dynamics to the case of lattice systems with unbounded linear spin spaces we first develop a general framework to discuss questions of this type using classical dirichlet forms on infinite dimensional state spaces and their associated diffusions we then describe concrete applications to lattice models with polynomial interactions i e the discretep d models of euclidean quantum field theory in addition we prove the equivalence of extremality and shift ergodicity for tempered gibbs states of these models and also discuss this question in the general framework

two simple proofs of the kochen specker theorem a new proof of the kochen specker theorem uses 33 rays instead of 117 in the original proof if the number of dimensions is increased from 3 to 4 only 24 rays are needed

the log sobolev inequality with quadratic interactions we assume one site measures without a boundary e x dx z that satisfies a log sobolev inequality we prove that if these measures are perturbed with quadratic interactions then the associated infinite dimensional gibbs measure on the lattice always satisfies a log sobolev inequality furthermore we present examples of measures that satisfy the inequality with a phase that goes beyond convexity at infinity

approximation integration and differentiation of time functions using a set of orthogonal hybrid functions hf and their application to solution of first order differential equations abstract differential equations of different types and orders are of utmost importance for mathematical modeling of control system problems state variable method uses the concept of expressing n number of first order differential equations in vector matrix form to model and analyze synthesize control systems the present work proposes a new set of orthogonal hybrid functions hf which evolved from synthesis of sample and hold functions shf and triangular functions tf this hf set is used to approximate a time function in a piecewise linear manner with the mean integral square error mise much less than block pulse function based approximation which always provides staircase solutions the operational matrices for integration and differentiation in hf domain are also derived and employed for solving non homogeneous and homogeneous differential equations of the first order as well as state equations the results are compared with exact solutions the 4th order runge kutta method and its further improved versions proposed by simos 6 the presented hf domain theory is well supported by a few illustrations

laguerre entire functions and the lee yang property laguerre entire functions are the polynomials of a single complex variable possessing real nonpositive zeros only or their limits on compact subsets of c these functions are employed to establish a property of isotropic i e o n invariant probability measures on r n email protected n it is called the lee yang property since in the case n 1 it corresponds to the property of the partition function of certain models of statistical physics first established by t d lee and c n yang a class of measures possessing this property is described certain connections of the lee yang property with other aspects of the analytic theory of probability measures are discussed

gibbs measures relative to brownian motion we consider brownian motion perturbed by the exponential of an action the action is the sum of an external one body potential and a two body interaction potential which depends only on the increments under suitable conditions on these potentials we establish existence and uniqueness of the corresponding gibbs measure we also provide an example where uniqueness fails because of a slow decay in the interaction potential

extremality and the global markov property ii the global markov property for non fkg maximal gibbs measures we give a condition on a gibbs measure for an attractive markov specification which assures extremality and the global markov property as an example of application we consider the class of attractive markov specifications defined on a compact configuration space over a two dimensional lattice by the interaction hamiltonians assumed to have a finite set of periodic ground configurations satisfying peierl s condition we prove that each extremal gibbs measure for such a specification at sufficiently low temperature has the global markov property

w kms structure from multi time euclidean green functions an axiomatic approach to the problem of reconstruction of a dynamics from the euclidean multi time green functions is proposed the existence of a w algebra on which the reconstructed dynamics acts as the canonical group of modular automorphisms is shown a condition under which the reconstruction from the one time and multi time green functions are equivalent is formulated

a priori estimates for symmetrizing measures and their applications to gibbs states abstract we prove existence and uniform a priori estimates for tempered gibbs states of certain classical lattice systems with unbounded spins nonharmonic pair potentials and infinite radius of interaction we use an alternative characterization of gibbs measures in terms of their radon nikodym derivatives w r t local shifts of the configuration space and corresponding integration by parts formulas

remarks on the non compact spin systems for an abstract thermodynamically well behaved local specification describing a lattice spin system with non compact state space the author gives a short proof of the independence of the limiting thermodynamics on the typical boundary conditions this general theorem is then applied to superstable and regular spin systems studied by lebowitz and presutti 1980 to simplify and clarify their proof another application gives the uniqueness theorem for the limiting gibbs phase for a class in general non superstable of lattice systems with unbounded spins

phase diagrams and cluster expansions for low temperature models i the phase diagram low temperature phase diagrams of two dimensional open image in new window quantum field models are constructed let open image in new window lie in an r 1 dimensional space of perturbations of a polynomial withr degenerate minima perform a scaling open image in new window and assume 1 we constructk distinct states on left begin array 20 c r k end array right hypersurfaces of codimensionk 1 in the space of perturbations an expansion is used to exhibit exponential clustering of the schwinger functions of each of these states at the core of the construction is a general technique for finding the thermodynamically stable phases from a collection of competing minima we draw on ideas of pirogov and sinai 24 for this problem

transfer function identification from impulse response via a new set of orthogonal hybrid functions hf the present work proposes a new set of hybrid functions hf which evolved from the synthesis of sample and hold functions shf and triangular functions tf traditional block pulse functions bpf still continue to be attractive to many researchers in the arena of control theory block pulse functions also gave birth to a few useful variants two such variants are shf and tf the former is efficient for analyzing sample and hold control systems while triangular functions established their superiority in obtaining piecewise linear solution of various control problems after developing the basic theory of hf a few square integrable functions are approximated via this set in a piecewise linear manner for such approximation it is shown the mean integral square error mise is much less than block pulse function based approximation the operational matrices for integration in hf domain are also derived finally this new set is employed for solving identification problem from impulse response data the results are compared with the solutions obtained via bpf shf tf etc and many illustrations are presented

simple unified form for the major no hidden variables theorems two examples are given that substantially simplify the no hidden variables theorem of kochen and specker greatly reducing the number of observables considered and requiring no intricate geometric argument while one of the examples also obeys a more powerful version of bell s theorem the other does not the examples provide a new perspective on both of these fundamental theorems and on the relation between them

bell kochen specker theorem for any finite dimension the bell kochen specker theorem against non contextual hidden variables can be proved by constructing a finite set of totally non colourable directions as kochen and specker did in a hilbert space of dimension n 3 we generalize kochen and specker s set to hilbert spaces of any finite dimension in a three step process that shows the relationship between different kinds of proofs continuum probabilistic state specific and state independent of the bell kochen specker theorem at the same time this construction of a totally non colourable set of directions in any dimension explicitly solves the question raised by zimba and penrose about the existence of such a set for n 5

maximal violation of bell inequalities for mixed states we show that mixed states can produce maximal violations in the bell inequality due to clauser horne shimony and holt chsh this follows from the degeneracy of the operator which is naturally associated with the bell inequality here called the bell operator we have calculated the form of all the eigenvalues for the generic chsh bell operator finally we consider several examples which demonstrate the utility of studying the eigenvalues and eigenvectors of the bell operator

translation invariant equilibrium states of ferromagnetic abelian lattice systems the structure of the set of all translation invariant equilibrium states is determined for all temperatures for which the free energy is differentiable models with several phase transitions are discussed rigorously

a quantum crystal with multidimensional anharmonic oscillators the quantum anharmonic crystal is made up of a large number of multidimensional anharmonic oscillators arranged in a periodic spatial lattice with a nearest neighbor coupling if the coupling coefficient is sufficiently small then there is a convergent expansion for the ground state of the crystal the estimates on the convergence are independent of the size of the crystal the proof uses the path integral representation of the ground state in terms of diffusion processes the convergence of the cluster expansion depends on the ergodicity properties of these processes

kochen specker theorem for finite precision spin one measurements unsharp spin one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains if the uncertainty is below a certain level and if the distribution of measurement errors is covariant under rotations a kochen specker theorem for the unsharp spin observables follows there are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way

numerical methods for ordinary differential equations in the 20th century abstract numerical methods for the solution of initial value problems in ordinary differential equations made enormous progress during the 20th century for several reasons the first reasons lie in the impetus that was given to the subject in the concluding years of the previous century by the seminal papers of bashforth and adams for linear multistep methods and runge for runge kutta methods other reasons which of course apply to numerical analysis in general are in the invention of electronic computers half way through the century and the needs in mathematical modelling of efficient numerical algorithms as an alternative to classical methods of applied mathematics this survey paper follows many of the main strands in the developments of these methods both for general problems stiff systems and for many of the special problem types that have been gaining in significance as the century draws to an end

phase transitions on nonamenable graphs we survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph most attention is devoted to transitive graphs and trees

fluctuations and their glauber dynamics in lattice systems abstract we consider a class of unbounded spin systems containing in particular anharmonic classical crystals and construct the stochastic dynamics in the space of macroscopic fluctuations starting from a given microscopic stochastic time evolution

stochastic processes associated with kms states abstract a general mathematical framework is presented for the connection between quantum statistical mechanics and periodic stochastic processes stochastically positive kms systems periodic os positive stochastic processes periodic positive semigroup structures are defined and shown to be equivalent the objects of the tomita takesaki theory are explicitly exhibited in terms of the associated stochastic process and the statements of the theory are proven a two sided markov property for the stochastic process is related to a cyclicity property of the kms state perturbations are constructed by the feynman kac nelson formula the general framework is applied to kms states given by density matrices

uniqueness of gibbs states for quantum lattice systems we prove uniqueness of euclidean gibbs states for certain quantum lattice systems with unbounded spins we use dobrushin s uniqueness criterion the necessary estimates for the vasershtein distance between the corresponding one point conditional distributions with boundary conditions differing only at one side are obtained by proving a log sobolev inequality on the infinite dimensional single spin loop spaces some important classes of concrete examples to which all this applies are discussed

compactness and the maximal gibbs state for random gibbs fields on a lattice we prove for a general class of gibbsian random field on that the set of tempered gibbs states is compact this class contains the euclidean random fields moreover if the interaction is attractive there is a unique minimal and maximal gibbs state and are unique translation invariant ant and have the global markov property we also prove that uniqueness of the tempered gibbs state is equivalent to the magnetizationsm qx being equal which is true if the pressure is differentiable

phase diagrams and cluster expansions for low temperaturep φ 2 models we give a cluster expansion for the schwinger functions of the stable phases found in part i the wightman axioms the mass gap and asymptoticity of perturbation theory follow

dirichlet forms and dirichlet operators for gibbs measures of quantum unbounded spin systems essential self adjointness and log sobolev inequality for each 0 1 we consider the dirichlet form mu gamma and the associated dirichlet operator h mu gamma for the gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential the gibbs measure is related to the gibbs state of the system via a functional euclidean integral procedure the configuration space for the spin systems is given by omega e mathbb z v e left omega in c left left 0 1 right mathbb r d right omega left 0 right omega left 1 right right we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the space under appropriate conditions on the potential we show that the dirichlet operator h mu left gamma right is essentially self adjoint on the domain of smooth cylinder functions we give sufficient conditions on the potential so that the corresponding gibbs measure is uniformly log concave ulc this property gives the spectral gap of the dirichlet operator h mu left gamma right at the lower end of the spectrum furthermore we prove that under the conditions of ulc the unique gibbs measure satisfies the log sobolev inequality ls we use an approximate argument used in the study of the same subjects for loop spaces which in turn is a modification of the method originally developed by s albeverio yu g kondratiev and m rockner

uniqueness and the global markov property for euclidean fields the case of general exponential interaction the uniqueness and the global markov property for the regular gibbs measure corresponding to the interaction u lambda varphi lambda int limits lambda d 2 x int d varrho alpha e alpha varphi 0 x for 0 d a probability measure with support in 2 sqrt pi 2 sqrt pi is proved

stochastic dynamics of fluctuations in classical continuous systems abstract fluctuations in classical continuous systems are studied in the low activity high temperature regime for these fluctuations a central limit theorem is proven and the space of macroscopic fluctuations is constructed furthermore it is shown that the generator of the microscopic stochastic dynamics in the fluctuation limit converges to the generator of a stochastic dynamics in the space of macroscopic fluctuations

kochen specker vectors some reference citations in the text of this paper are incorrect and should be amended as listed below the reference list is correct as published page 1579 line 5 23 34 38 39 should read 23 34 35 36 page 1579 line 9 40 should read 37 page 1580 line 8 31 33 35 should read 31 33 38 page 1580 line 14 36 should read 39 page 1580 line 36 36 should read 39 page 1580 line 38 37 should read 40 page 1580 line 42 38 should read 35 page 1581 line 3 of caption 33 35 should read 33 38 page 1583 line 12 41 should read 42 page 1587 line 9 39 should read 36 page 1587 line 11 39 should read 36 page 1587 line 18 38 39 should read 35 36 page 1587 line 37 39 should read 36 page 1589 line 18 39 46 47 should read 36 46 47 page 1590 line 2 39 should read 36 age 1590 line 3 39 should read 36

ground state for point particles interacting through a massless scalar bose field we consider a massless scalar bose field interacting with two particles one of them infinitely heavy neither an infrared nor an ultraviolet cutoff is imposed in case the charge of the particles is of the same sign and sufficiently small we prove the existence of a ground state

dobrushin s uniqueness for quantum lattice systems with nonlocal interaction based on dobrushin s fundamental criterion we prove uniqueness of euclidean gibbs states for a certain class of quantum lattice systems with unbounded spins nonharmonic pair potentials and infinite radius of interaction the necessary estimates on dobrushin s coefficients are obtained from the log sobolev inequality which holds for the one point conditional distributions on the infinite dimensional single spin loop spaces

uniqueness and clustering properties of gibbs states for classical and quantum unbounded spin systems we consider quantum unbounded spin systems lattice boson systems in dimensional lattice space z under appropriate conditions on the interactions we prove that in a region of high temperatures the gibbs state is unique is translationally invariant and has clustering properties the main methods we use are the wiener integral representation the cluster expansions for zero boundary conditions and for general gibbs state and explicitly dependent probability estimates for one dimensional systems we show the uniqueness of gibbs states for any value of temperature by using the method of perturbed states we also consider classical unbounded spin systems we derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case

dirichlet operators via stochastic analysis abstract we give sufficient conditions for essential self adjointness of symmetric differential operators dirichlet operators associated with classical dirichlet forms given by probability measures on hilbert spaces under an additional assumption of log concavity for the measures we prove the existence of a gap at the lower end of spectrum of the dirichlet operator and the ergodicity of the corresponding semi group we consider also applications to the study of stochastic dynamics in some classical lattice systems

numerical solution of third order linear differential equations using generalized one shot operational matrices in orthogonal hybrid function domain abstract the present work proposes a new set of orthogonal hybrid functions hf which evolved from synthesis of orthogonal sample and hold functions shf and triangular functions tf the hf set is used to approximate a time function in a piecewise linear manner for such approximation the mean integral square error mise is much less than block pulse function based approximation which always provides staircase solutions and it is found that hf based approximation is a strong contender of approximations based upon orthogonal polynomials like legendre polynomials the respective mise s and elapsed times for mise computations for these three kinds of approximations are also studied in detail the one shot operational matrices for integration of different orders in hf domain are also derived these matrices are employed for more accurate multiple integration an example is treated to determine efficiency of these matrices finally these matrices are employed for solving third order non homogeneous differential equations followed by a numerical example the results obtained via matlab are compared with the exact solution as well as the results obtained via 4th order runge kutta method

uniqueness of gibbs states for general p ϕ 2 weak coupling models by cluster expansion we consider quantum fields with weak coupling in two space time dimensions we prove that the set of their ultraregular gibbs states consists of only one point and this point is an extremal gibbs state

glauber dynamics of fluctuations we derive the time evolution of the normal fluctuations of a classical lattice spin system induced by a generalized glauber dynamics the canonical form of this dynamics is derived we prove that it is asymptotically i e after the central limit free the results are applied to give a rigorous proof of the macroscopic reciprocity relations and the linear theory for small deviations from equilibrium

ergodicity for the stochastic dynamics of quasi invariant measures with applications to gibbs states the convex set maof quasi invariant measures on a locally convex spaceewith given shift radon nikodym derivatives i e cocycles a atk k k0 t ris analyzed the extreme points of maare characterized and proved to be non empty a specification of lattice type is constructed so that macoincides with the set of the corresponding gibbs states as a consequence via a well known method due to dynkin and follmer a unique representation of an arbitrary element in main terms of extreme ones is derived furthermore the corresponding classical dirichlet forms e d e and their associated semigroups t t t 0onl2 e are discussed under a mild positivity condition it is shown that mais extreme if and only if e d e is irreducible or equivalently t t t 0is ergodic this implies time ergodicity of associated diffusions applications to gibbs states of classical and quantum lattice models as well as those occuring in euclidean quantum field theory are presented in particular it is proved that the stochastic quantization of a guerra rosen simon gibbs state on d r2 ininfinite volumewith polynomial interaction is ergodic if the gibbs state is extreme i e is a pure phase which solves a long standing open problem

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

euclidean gibbs measures of interacting quantum anharmonic oscillators a rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting dimensional quantum anharmonic oscillators is given the oscillators are indexed by the elements of a countable set mathbb l subset mathbb r d possibly irregular the anharmonic potentials vary from site to site and the interaction has infinite range the description is based on the representation of the gibbs states in terms of path measures the so called euclidean gibbs measures it is proven that a the set of such measures mathcal g rm t is non void and compact b every mu in mathcal g rm t obeys an exponential integrability estimate the same for the whole set mathcal g rm t c every mu in mathcal g rm t has a lebowitz presutti type support d mathcal g rm t is a singleton at high temperatures the case of attractive interaction and nu 1 is studied in more detail we prove that a mathcal g rm t 1 at low temperatures b mathcal g rm t 1 due to quantum effects and at a nonzero external field thereby a qualitative theory of phase transitions and quantum effects which interprets most important experimental data known for the corresponding physical objects is developed

small mass implies uniqueness of gibbs states of a quantum crystal a model of interacting quantum particles performing one dimensional anharmonic oscillations around their equilibrium positions which form a lattice d is considered for this model it is proved that the set of tempered euclidean gibbs measures is a singleton provided the particle mass is less than a certain bound m which is independent of the temperature 1 this settles a problem that was open for a long time and is an essential improvement of a similar result proved before by the same authors 5 where the bound m depended on in such a way that m ast beta rightarrow 0 as beta rightarrow infty

free energy density for continuous systems with and without superstability assumptions the thermodynamic limit of the free energy density for a large class of continuous charged systems with stable and sufficiently regular many body forces is studied the main effort is placed on demonstrating rigorously that thermodynamic functions do not depend on the typical boundary conditions among the results the most important and new ones are the following 1 for any superstable or superstable in an extended sense and sufficiently regular many body interactions the thermodynamic limit of the conditioned free energy density exists and is equal to that corresponding to the free boundary condition case 2 a new criterion for the nondependence of the limiting free energy density on the typical boundary condition is formulated and proved this criterion does not require any superstability type of assumptions among several applications of the results we list only two a to the case of two dimensional neutral yukawa gas in the monopole phase which is not even stable according to the standard no

invariance implies gibbsian some new results we investigate stationary distributions of stochastic gradient systems in riemannian manifolds and prove that under certain assumptions such distributions are symmetric these results are extended to countable products of finite dimensional manifolds and applied to gibbs distributions in the case where the single spin spaces are riemannian manifolds in particular we obtain a new result concerning the question whether all invariant measures are gibbsian actually we consider a more general object weak elliptic equations for measures which on the one hand yields the results obtained stronger than the above mentioned statements and on the other hand enables us to give simpler proofs of more general than previously known facts applications to concrete models of lattice systems over d with not necessarily compact spin space are presented also in the case d 3 under certain assumptions of decay of interaction

functional integral representations of the pauli fierz model with spin 1 2 a feynman kac type formula for a levy and an infinite dimensional gaussian random process associated with a quantized radiation field is derived in particular a functional integral representation of e thpf generated by the pauli fierz hamiltonian with spin 1 2 in non relativistic quantum electrodynamics is constructed when no external potential is applied hpf turns translation invariant and it is decomposed as a direct integral hpf r3 hpf p dp the functional integral representation of e thpf p is also given although all these hamiltonians include spin nevertheless the kernels obtained for the path measures are scalar rather than matrix expressions as an application of the functional integral representations energy comparison inequalities are derived

on the dlr equation for the two dimensional sine gordon model the dobrushin lanford ruelle equation is studied in a certain space of measures in the case of two dimensional trigonometric interactions the uniqueness theorem extending the results of albeverio and hoegh krohn s albeverio and r hoegh krohn commun math phys 68 95 1979 is proved the extension is obtained by the application of some correlation inequalities of the ginibre type which reduce the proof of the uniqueness of the translationally invariant regular tempered gibbs states to the question on the independence of the infinite volume free energy of the boundary conditions the required independence is proved in this paper

the global markov property for equilibrium states which are determined by correlations in a strip consider an interaction round face potential on the lattice d which may include nearest neighbor and next nearest neighbor pair interactions as well as more general plaquette terms assuming some periodicity of the potential it is shown that under the condition that equilibrium states can be distinguished by expectation values of sufficiently local observables equilibrium states possess a global markov property the condition under which this markov property is shown to hold is met in particular in case the equilibrium state is unique or determined by the magnetization the proof is based on an application of the variational principle to states which are constructed like markov chains

phase transitions and algebra of fluctuation operators in an exactly soluble model of a quantum anharmonic crystal a complete description of the fluctuation operator algebra is given for a quantum crystal showing displacement structural phase transitions in the one phase region the fluctuations are normal and its algebra is non abelian in the two phase region and on the critical line t c 0 the momentum fluctuation is normal the displacement is critical and the algebra is abelian att c 0 quantum phase transition this algebra is non abelian with abnormal displacement and supernormal squeezed momentum fluctuation operators both being dimension dependent