critical phenomena and universal exponents in statistical physics on dyson s hierarchical model on etudie le comportement des etats de gibbs a la temperature critique ou a proximite on etudie en details le modele hierarchique de dyson et on presente les plus importants resultats

multiparametric linear programming support set and optimal partition invariancy traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis interior point methods however do not converge to a basic solution vertex in general recently there appeared new techniques in sensitivity analysis which consist in preserving so called support set invariancy and optimal partition invariancy this paper reflects the renascence of sensitivity and parametric analysis and extends single parametric results to the case when there are multiple parameters in the objective function and in the right hand side of equations multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does we present a description of the set of admissible parameters under the mentioned invariances and compare them with the classical optimal basis concept

simultaneous primal dual right hand side sensitivity analysis from a strictly complementary solution of a linear program this paper establishes theorems about the simultaneous variation of right hand sides and cost coefficients in a linear program from a strictly complementary solution some results are extensions of those that have been proven for varying the right hand side of the primal or the dual but not both other results are new in addition changes in the optimal partition and what that means in economic terms are related to the basis driven approach notably to the theory of compatibility in addition to new theorems about this relation the transition graph is extended to provide another visualization of the underlying economics

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

a hierarchical model of quantum anharmonic oscillators critical point convergence a hierarchical model of interacting quantum particles performing anharmonic oscillations is studied in the euclidean approach in which the local gibbs states are constructed as measures on infinite dimensional spaces the local states restricted to the subalgebra generated by fluctuations of displacements of particles are in the center of the study they are described by means of the corresponding temperature green matsubara functions the result of the paper is a theorem which describes the critical point convergence of such matsubara functions in the thermodynamic limit

on the iterates of positive linear operators preserving the affine functions in this note we study the limit behavior of the iterates of a large class of positive linear operators preserving the affine functions and as a byproduct of our result we obtain the limit of the iterates of meyer konig and zeller operators

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

non gaussian fixed points of the block spin transformation hierarchical model approximation with the use of analyticity techniques recently developed by the authors the e and 1 n expansion type arguments are turned into a rigorous control of the non gaussian fixed point of the hierarchical model renormalization group the present approach should extend beyond the hierarchical approximation and result in mathematical theory of the critical point of statistical mechanics or quantum field theory in three dimensions for small e or largen

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

yang lee circle theorem for an ideal pseudospin 1 2 bose gas in an arbitrary external potential and in an external magnetic field abstract yang lee circle theorem was extended to an ideal homogeneous pseudospin 1 2 bose gas in an external magnetic field x z wang phys rev e 63 2001 046103 in this paper the theorem is extended to the case with an arbitrary external potential the densities of zeros for several cases are determined it is found that the critical exponents of the yang lee edge singularities are the mean field values 1 2 independent of external potentials and spatial dimensions

on the convergence of the central path in semidefinite optimization the central path in linear optimization always converges to the analytic center of the optimal set this result was extended to semidefinite optimization in d goldfarb and k scheinberg siam j optim 8 1998 pp 871 886 in this paper we show that this latter result is not correct in the absence of strict complementarity we provide a counterexample where the central path converges to a different optimal solution this unexpected result raises many questions we also give a short proof that the central path always converges in semidefinite optimization by using ideas from algebraic geometry

multi parameter surfaces of analytic centers and long step surface following interior point methods we develop a long step polynomial time version of the method of analytic centers for non linear convex problems the method traces a multi parameter surface of analytic centers rather than the usual path which allows to handle cases with noncentered and possibly infeasible starting point

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

on the spectrum of positive linear operators with a partition of unity property abstract we characterize the spectrum of positive linear operators between banach function spaces having finite rank and a partition of unity property our main result states that all the points in the spectrum are eigenvalues and 1 is the only eigenvalue on the unit circle finally we show that the iterates converge in the uniform operator topology to a projection operator that reproduces constant functions and we provide a simple criterion to obtain the limiting projection operator

complex temperature plane zeros in the mean field approximation we derive asymptotic expressions for the complex temperature plane zeros of the infinite range ising model in the scaling regime the results also apply to high dimensional short range ising systems for thenth zero in a system ofn spins the leading asymptotic result istn n n 1 2 1 i

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

analytic centers and repelling inequalities the new concepts of repelling inequalities repelling paths and prime analytic centers are introduced a repelling path is a generalization of the analytic central path for linear programming and we show that this path has a unique limit furthermore this limit is the prime analytic center if the set of repelling inequalities contains only those constraints that shape the polytope because we allow lower dimensional polytopes the proof techniques are non standard and follow from data perturbation analysis this analysis overcomes the difficulty that analytic centers of lower dimensional polytopes are not necessarily continuous with respect to the polytope s data representation a second concept introduced here is that of the prime analytic center in which we establish its uniqueness in the absence of redundant inequalities again this is well known for full dimensional polytopes but it is not immediate for lower dimensional polytopes because there are many different data representations of the same polytope each without any redundant inequalities these two concepts combine when we introduce ways in which repelling inequalities can interact

renormalization of dyson s hierarchical vector valued φ 4 model at low temperatures we investigate dyson s hierarchical vector valued 4 model at low temperatures the case 2 c sqrt 2 is considered the pure phase is constructed and the existence of its large scale limit is proved the limit is gaussian but an unusual normalization has to be chosen in the direction of the spontaneous magnetization one has to divide by the square root of the volume but in the orthogonal direction one has to divide by a different power of the volume for all low temperatures

asymptotic properties of powers of linear positive operators which preserve e2 in this paper we prove korovkin type theorem for iterates of general positive linear operators t c 0 1 c 0 1 which preserve e 2 and derive quantitative estimates in terms of moduli of smoothness the results can be applied to several well known operators we present here the bernstein the q bernstein the genuine bernstein durrmeyer and the genuine q bernstein durrmeyer operators

a nonlinear dynamical system on the set of laguerre entire functions a nonlinear modification of the cauchy problem dtf t z dzf t z zd 2 zf t z t ir 0 z c 0 f 0 z g z l is considered the set l consists of laguerre entire functions which one obtains as a closure of the set of polynomials having real nonpositive zeros only in the topology of uniform convergence on compact subsets of c the modification means that the time half line ir is divided onto the intervals in n 1 n n in 0 and on each in the evolution is to be described by the above equation but at the endpoints the function f t z is changed f n z

simultaneous data perturbations and analytic center convergence the central path is an infinitely smooth parameterization of the nonnegative real line and its convergence properties have been investigated since the mid 1980s however the central path followed by an infeasible interior point method relies on three parameters instead of one and hence is a surface instead of a path the additional parameters are included to allow for simultaneous perturbations in the cost vectors and right hand side vectors this paper provides a detailed analysis of the perturbed central path that is followed by infeasible interior point methods and we characterize when such a path converges we develop a set hausdorff convergence property and show that the central paths impose an equivalence relation on the set of admissible cost vectors we conclude with a technique to test for convergence under arbitrary simultaneous data perturbations

sensitivity analysis in linear semi infinite programming perturbing cost and right hand side coefficients this paper analyzes the effect on the optimal value of a given linear semi infinite programming problem of the kind of perturbations which more frequently arise in practical applications those which affect the objective function and the right hand side coefficients of the constraints in particular we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation

a general parametric analysis approach and its implication to sensitivity analysis in interior point methods adler and monteiro 1992 developed a parametric analysis approach that is naturally related to the geometry of the linear program this approach is based on the availability of primal and dual optimal solutions satisfying strong complementarity in this paper we develop an alternative geometric approach for parametric analysis which does not require the strong complementarity condition this parametric analysis approach is used to develop range and marginal analysis techniques which are suitable for interior point methods two approaches are developed namely the lu factorization approach and the affine scaling approach

sensitivity analysis in linear programming and semidefinite programming using interior point methods we analyze perturbations of the right hand side and the cost parameters in linear programming lp and semidefinite programming sdp we obtain tight bounds on the perturbations that allow interior point methods to recover feasible and near optimal solutions in a single interior point iteration for the unique nondegenerate solution case in lp we show that the bounds obtained using interior point methods compare nicely with the bounds arising from using the optimal basis we also present explicit bounds for sdp using the monteiro zhang family of search directions and specialize them to the aho h k m and nt directions

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

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

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

yang lee edge singularity of a one dimensional ising ferromagnet with arbitrary spin it is shown that for a one dimensional lattice system in a purely imaginary magnetic field if the interaction is finite range the nature of the yang lee edge singularity is universal independent of the spin and interaction strengths the edge singularity corresponds to the twofold degeneracy of the largest eigenvalues of the transfer matrix for the blume emery griffiths ferromagnet the tricritical point and the edge pseudosingularity may exist the tricritical point corresponds to the triple degeneracy of the eigenvalues the edge pseudosingularity corresponds to the twofold degeneracy of the nonlargest eigenvalues

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

ifs on a metric space with a graph structure and extensions of the kelisky rivlin theorem abstract we develop the hutchinson barnsley theory for finite families of mappings on a metric space endowed with a directed graph in particular our results subsume a classical theorem of j e hutchinson j e hutchinson fractals and self similarity indiana univ math j 30 1981 713 747 on the existence of an invariant set for an iterated function system of banach contractions and a theorem of l mate l mate the hutchinson barnsley theory for certain non contraction mappings period math hungar 27 1993 21 33 concerning finite families of locally uniformly contractions introduced by edelstein also they generalize recent fixed point theorems of a c m ran and m c b reurings a c m ran m c b reurings a fixed point theorem in partially ordered sets and some applications to matrix equations proc amer math soc 132 2004 1435 1443 j j nieto and r rodriguez lopez j j nieto r rodriguez lopez contractive mapping theorems in partially ordered sets and applications to ordinary differential equations order 22 2005 223 239 j j nieto r rodriguez lopez existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations acta math sin engl ser 23 2007 2205 2212 and a petrusel and i a rus a petrusel i a rus fixed point theorems in ordered l spaces proc amer math soc 134 2006 411 418 for contractive mappings on an ordered metric space as an application we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary banach space this result yields new generalizations of the kelisky rivlin theorem on iterates of the bernstein operators on the space c 0 1 as well as its extensions given recently by h oruc and n tuncer h oruc n tuncer on the convergence and iterates of q bernstein polynomials j approx theory 117 2002 301 313 and h gonska and p pi ul h gonska p pi ul remarks on an article of j p king comment math univ carolin 46 2005 645 652

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

sensitivity analysis in linear semi infinite programming via partitions this paper provides sufficient conditions for the optimal value function of a given linear semi infinite programming lsip problem to depend linearly on the size of the perturbations when these perturbations involve either the cost coefficients or the right hand side function or both and they are sufficiently small two kinds of partitions are considered the first concerns the effective domain of the optimal value as a function of the cost coefficients and consists of maximal regions on which this value function is linear the second class of partitions considered in this paper concerns the index set of the constraints through a suitable extension of the concept of optimal partition from ordinary to lsip these partitions provide convex sets in particular segments on which the optimal value is a linear function of the size of the perturbations for the three types of perturbations considered in this paper

on the complexity of following the central path of linear programs by linear extrapolation ii a class of algorithms is proposed for solving linear programming problems withm inequality constraints by following the central path using linear extrapolation with a special adaptive choice of steplengths the latter is based on explicit results concerning the convergence behaviour of newton s method to compute points on the central pathx r r 0 and this allows to estimate the complexity i e the total numbern n r of steps needed to go from an initial pointx r to a final pointx r 0 by an integral of the local weighted curvature of the primal dual path here the central curve is parametrized with the logarithmic penalty parameterr 0 it is shown that for large classes of problems the complexity integral i e the number of stepsn is not greater than constm log r where 1 2 e g 1 4 or 3 8 note that 1 2 gives the complexity of zero order methods we also provide a lower bound for the complexity showing that for some problems the above estimation can hold only for 1 3 as a byproduct many analytical and structural properties of the primal dual central path are obtained there are for instance close relations between the weighted curvature and the logarithmic derivatives of the slack variables the dependence of these quantities on the parameterr is described also related results hold for a family of weighted trajectories into which the central path can be embedded

applications of the notion of analytic center in approximation estimation problems abstract a new method for solving a set of linear inequalities based on a generalization of the central maximum entropy solution of moment problems is applied to problems of numerical approximation cubature and filtering

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

on the iterates of some bernstein type operators abstract in this paper we establish two basic functional type identities between the iterates of the bleimann butzer hahn operator and those of the bernstein operator on the one hand and the iterates of the modified meyer konig and zeller operator and those of the baskakov operator on the other these identities allow us to transfer the properties of these operators from one to another attention is focused on the limit behavior of the iterates and the linear combinations of iterates of fejer korovkin type

partition function zeros for the ising model on complete graphs and on annealed scale free networks we analyse the partition function of the ising model on graphs of two different types complete graphs wherein all nodes are mutually linked and annealed scale free networks for which the degree distribution decays as p k k we are interested in zeros of the partition function in the cases of complex temperature or complex external field fisher and lee yang zeros respectively for the model on an annealed scale free network we find an integral representation for the partition function which in the case 5 reproduces the zeros for the ising model on a complete graph for 3 5 we derive the dependent angle at which the fisher zeros impact onto the real temperature axis this in turn gives access to the dependent universal values of the critical exponents and critical amplitudes ratios our analysis of the lee yang zeros reveals a difference in their behaviour for the ising model on a complete graph and on an annealed scale free network when 3 5 whereas in the former case the zeros are purely imaginary they have a non zero real part in latter case so that the celebrated lee yang circle theorem is violated

hierarchical ferromagnetic vector spin model possessing the lee yang property thermodynamic limit at the critical point and above the hierarchical ferromagneticn dimensional vector spin model as a sequence of probability measures onrn is considered the starting element of this sequence is chosen to belong to the lee yang class of measures that is defined in the paper and includes most known examples 4 measures gaussian measures and so on for this model we probe two thermodynamic limit theorems one of them is just the classical central limit theorem for weakly dependent random vectors it describes the convergence of classically normed sums of spins when temperature is sufficiently high the other theorem describes the convergence of more than normally normed sums that holds for some fixed temperature it corresponds to the strong dependence of spins which appears at the critical point of the model

an interior point approach to sensitivity analysis in degenerate linear programs we consider an interior point approach to sensitivity analysis in linear programming developed by the authors we investigate the quality of the interior point bounds under degeneracy in the case of a special type of degeneracy we show that these bounds have the same nice asymptotic relationship with the optimal partition bounds as in the nondegenerate case we prove a weaker relationship for general degenerate linear programs

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

on the dimension of the set of rim perturbations for optimal partition invariance two new dimension results are presented for linear programs it is shown that the sum of the dimension of the optimal set and the dimension of the set of objective perturbations for which the optimal partition is invariant equals the number of variables a decoupling principle shows that the primal and dual results are additive the main result is then extended to convex quadratic programs but the dimension relationships are no longer dependent only on problem size furthermore although the decoupling principle does not extend completely the dimensions are additive as in the linear case

first and second order phase transitions in scale free networks we study first and second order phase transitions of ferromagnetic lattice models on scale free networks with a degree exponent gamma using the example of the q state potts model we derive a general self consistency relation within the frame of the weiss molecular field approximation which presumably leads to exact critical singularities depending on the value of gamma we have found three different regimes of the phase diagram as a general trend first order transitions soften with decreasing gamma and the critical singularities at the second order transitions are gamma dependent

the strength of first and second order phase transitions from partition function zeroes we present a numerical technique employing the density of partition function zeroes i to distinguish between phase transitions of first and higher order ii to examine the crossover between such phase transitions and iii to measure the strength of first and second order phase transitions in the form of latent heat and critical exponents these techniques are demonstrated in applications to a number of models for which zeroes are available

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

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

an interior point perspective on sensitivity analysis in semidefinite programming we study the asymptotic behavior of the interior point bounds arising from the work of yildirim and todd on sensitivity analysis in semidefinite programming in comparison with the optimal partition bounds we introduce a weaker notion of nondegeneracy and discuss its implications for perturbations of the right hand side vector or the cost matrix we show that the interior point bounds evaluated on the central path using the monteiro zhang family of search directions converge as the duality gap tends to zero to the symmetrized version of the optimal partition bounds under mild nondegeneracy assumptions furthermore our analysis does not assume strict complementarity as long as the central path converges to the analytic center in a relatively controlled manner we also show that the same convergence results carry over to iterates lying in an appropriate very narrow central path neighborhood if the nesterov todd direction is used to evaluate the interior point bounds we extend our results to the case of simultaneous perturbations of the right hand side vector and the cost matrix we also provide examples illustrating that our assumptions in general cannot be weakened

critical behavior of the ising model in annealed scale free networks we study the critical behavior of the ising model in annealed scale free sf networks of finite system size with forced upper cutoff in degree by mapping the model onto the weighted fully connected ising model we derive analytic results for the finite size scaling fss near the phase transition characterized by the cutoff dependent two parameter scaling with four distinct scaling regimes in highly heterogeneous networks these results are essentially the same as those found for the nonequilibrium contact process in annealed sf networks except for an additional complication due to the trivial critical point shift in finite systems the discrepancy of the fss theories between annealed and quenched sf networks still remains in the equilibrium ising model like some other nonequilibrium models all of our analytic results are confirmed reasonably well by numerical simulations

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

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