weak singularity and absence of metastability in random ising ferromagnets in the above models there exists a weak singularity of the magnetisation in addition to its jump on the first order transition line it corresponds to the griffiths 1969 singularity above the temperature of the phase transition analytic continuation from positive to negative magnetic fields yielding a metastable state is impossible

a competitive comparison of multiparameter stacking operators abstractthe classic common midpoint cmp stack which sums along offsets suffers in challenging environments in which the acquisition is sparse in the past several multiparameter stacking techniques were introduced that incorporate many neighboring cmps during summation this increases data redundancy and reduces noise multiparameter methods that can be parameterized by the same wavefront attributes are multifocusing mf the common reflection surface crs implicit crs and nonhyperbolic crs ncrs the crs type operators use a velocity shift mechanism to account for heterogeneity by changing the slope of the asymptote on the other hand mf uses a different mechanism a shift of reference time while preserving the slope of the asymptote we have formulated mf such that it uses the same mechanism as the crs type operators and compare them on a marine data set in turn we investigate the behavior of time shifted versions of the crs type approximations to provide a fair comparison we use a global

improved perturbation expansion for disordered systems beating griffiths singularities we introduce a new expansion to prove exponential clustering of connected correlations in a large class of disordered systems our expansion converges for values of the temperature and magnetic field where standard cluster expansions diverge due to the presence of griffiths type singularities it is organized inductively over an infinite sequence of increasing distance scales in each induction step one redefines what is means by the unperturbed system a procedure somewhat reminiscent of k a m theory our techniques may be useful in dealing with the so called large field problem in real space renormalization group schemes

rounding effects of quenched randomness on first order phase transitions frozen in disorder in an otherwise homogeneous system is modeled by interaction terms with random coefficients given by independent random variables with a translation invariant distribution for such systems it is proven that ind 2 dimensions there can be no first order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter discontinuities which would amount to a continuous symmetry breaking in systems which are stochastically invariant under the action of a continuous subgroup ofo n are suppressed by the randomness in dimensionsd 4 specific implications are found in the random field ising model for which we conclude that ind 2 dimensions at all h the gibbs state is unique for almost all field configurations and in the random bond potts model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point the results are explained by the argument of imry and ma 1 the proofs involve the analysis of fluctuations of free energy differences which are shown using martingale techniques to be gaussian on the suitable scale

renormalization group in the uniqueness region weak gibbsianity and convergence we analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature we prove weak gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system the correlation length or the critical length for metastability or both thus to perturbatively treat the problem we have to use a scale adapted expansion moreover such a model below the critical temperature resembles a disordered system in the presence of griffiths singularity then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached

phase uniqueness and correlation length in diluted field ising models the diluted field ising model a random nonnegative field ferromagnetic model is shown to have a unique gibbs measure with probability i when the field mean is positive our methods involve comparisons with ordinary uniform field ising models they yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field the correlation lengths of this model defined as limn 1 n log 0 n 1 wheren is the site on the first coordinate axis at distancen from the origin and 0 n is the origin ton two point truncated correlation function is non random we derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model

fluctuations of extensive functions of quenched random couplings an extensive quantity is a family of functions v of random parameters indexed by the finite regionsv subsets of d over which v are additive up to corrections satisfying the boundary estimate stated below it is shown that unless the randomness is nonessential in the sense that lim v v has a unique value in the absolute i e not just probabilistic sense the variance of such a quantity grows as the volume ofv of particular interest is the free energy of a system with random couplings for such v bounds are derived also for the generating functione et in a separate application variance bounds are used for an inequality concerning the characteristic exponents of directed polymers in a random environment

computing true amplitude reflections in a laterally inhomogeneous earth recently bortfeld 1982 gave a cursory nonmathematical introduction to a procedure for computing the geometrical spreading factor of a primary zero offset reflection from the common datum point traveltime measurements of the event to underline the significance and consequences of this method a derivation and discussion of geometrical spreading factors is now given for two and three dimensional earth models with curved reflecting boundaries the spreading factors can be used easily to transform primary reflections in a zero offset seismic section to true amplitude reflections these permit an estimation of interface reflection coefficients either directly or in connection with a true amplitude migration a seismic section with true amplitude reflections can be described by one physical experiment the tuned reflector model hence the application of the wave equation in connection with a migration after stack is justified on such a seismic section also the geometrical spreading factors that are deri

kms states and the chemical potential for disordered systems we extend the theory of the chemical potential associated to a compact separable gauge group to the case of disordered quantum systems this is done in the framework of operator algebras among the other results we show that the chemical potential does not depend on the disorder the situation of the n torus is treated in some detail indeed the chemical potential is intrinsically defined in terms of the direct integral decomposition of the connes radon nikodym cocycle associated to the normal extension of the kms state and its trasforms by the localized automorphisms of the observable algebra carrying the abelian charges of the model under consideration this description parallels the analogous one relative to the usual i e non disordered quantum models

phase transition in the 1d random field ising model with long range interaction we study one dimensional ising spin systems with ferromagnetic long range interaction decaying as n 2 alpha in left frac 12 frac ln 3 ln2 1 right in the presence of external random fields we assume that the random fields are given by a collection of symmetric independent identically distributed real random variables gaussian or subgaussian we show for temperature and strength of the randomness variance small enough with ip 1 with respect to the random fields that there are at least two distinct extremal gibbs measures

almost gibbsian description of the sign fields of sos fields an example is presented of a measure on a lattice system which has a measure zero set of points configurations where some conditional probability can be discontinuous but does not become a gibbs measure under decimation or other transformations we also discuss some related issues

stochastic symmetry breaking in a gaussian hopfield model we study a two pattern hopfield model with gaussian disorder we find that there are infinitely many pure states at low temperatures in this model and that the metastate is supported on an infinity of symmetric pairs of pure states the origin of this phenomenon is the random breaking of a rotation symmetry of the distribution of the disorder variables

the kac version of the sherrington kirkpatrick model at high temperatures we study the kac version of the sherrington kirkpatrick sk model of a spin glass i e a spin glass with long but finite range interaction on mathbb z d and gaussian mean zero couplings we prove that for all 1 the free energy of this model converges to that of the sk model as the range of the interaction tends to infinity moreover we prove that for all temperatures for which the infinite volume gibbs state is unique the free energy scaled by the square root of the volume converges to a gaussian with variance c where 1 is the range of the interaction moreover at least for almost all values of this variance tends to zero as goes to zero the value in the sk model we interpret our finding as a weak indication that at least at high temperatures the sk model can be seen as a reasonable asymptotic model for lattice spin glasses

numerical ranges of large toeplitz matrices abstract a bananch algebraic approach is proposed to study the asymptotic behaviour of the numerical ranges of certain finite approximation matrices of infinite operators the approach works for large classes of approximation methods it is examined in detail here for the finite sections of toeplitz operators and of operators which are generated by toeplitz operators the basic ingredient is a precise knowledge of the finite section method for toeplitz and related operators

energy entropy inequalities for classical lattice systems a new characterization of equilibrium states for classical lattice systems is given in terms of correlation inequalities their physical meaning is found to express thermodynamic stability we demonstrate the applicability of the inequalities in specific models

normal moveout revisited inhomogeneous media and curved interfaces the equation of normal moveout t2 t02 x2 va2 is valid for a reflection from the base of a single homogeneous and isotropic bed but is only an approximation in the real world of multilayered inhomogeneous media and curved interfaces using the theory of geometrical optics we can find another second order equation which represents hyperbolas that are also symmetrical about the time axis however the centers of these hyperbolas do not coincide with the center of coordinates but are shifted along the time axis the equation describing this second type of hyperbola is t tp t0 2 tp2 x2 v12 where tp is the time of focusing depth and v1 the velocity of the input medium this equation is not only more accurate than the usual normal moveout but its use is more economical on a vector computer because the traditional dynamic correction is a static correction in the tp analysis this procedure makes it possible to compute velocities for all the samples of all the stacked traces and produces a velocity secti

relaxation to equilibrium for two dimensional disordered ising systems in the griffiths phase we consider glauber type dynamics for two dimensional disordered magnets of ising type we prove that if the disorder averaged influence of the boundary condition is sufficiently small in the equilibrium system then the corresponding glauber dynamics is ergodic with probability one and the disorder average c t of time autocorrelation function satisfies for large t for the standard two dimensional dilute ising ferromagnet with i i d random nearest neighbor couplings taking the values 0 or j 0 0 our results apply even if the active bonds percolate and j 0 is larger than the critical value j c of the corresponding pure ising model for the same model we also prove that in the whole griffiths phase the previous upper bound is optimal this implies the existence of a dynamical phase transition which occurs when j crosses j c

limiting measure of lee yang zeros for the cayley tree this paper is devoted to an in depth study of the limiting measure of lee yang zeroes for the ising model on the cayley tree we build on previous works of muller hartmann and zittartz z phys b 22 59 1975 muller hartmann z phys b 27 161 168 1977 barata and marchetti j stat phys 88 231 268 1997 and barata and goldbaum j stat phys 103 857 891 2001 to determine the support of the limiting measure prove that the limiting measure is not absolutely continuous with respect to lebesgue measure and determine the pointwise dimension of the measure at lebesgue a e point on the unit circle and every temperature the latter is related to the critical exponents for the phase transitions in the model as one crosses the unit circle at lebesgue a e point providing a global version of the phase transition of continuous order discovered by muller hartmann zittartz the key techniques are from dynamical systems because there is an explicit formula for the lee yang zeros of the finite cayley tree of level n in terms of the n th iterate of an expanding blaschke product a subtlety arises because the conjugacies between blaschke products at different parameter values are not absolutely continuous

percolation techniques in disordered spin flip dynamics relaxation to the unique invariant measure we consider lattice spin systems with short range but random and unbounded interactions we give criteria for ergodicity of spin flip dynamics and estimate the speed of convergence to the unique invariant measure we find for this convergence a stretched exponential in time for a class of directed dynamics such as in the disordered toom or stavskaya model for the general case we show that the relaxation is faster than any power in time no assumptions of reversibility are made the methods are based on relating the problem to an oriented percolation problem contact process and for the general case using a slightly modified version of the multiscale analysis of e g klein 1993

singularities of the effective fugacity on the ising model on the cayley tree abstract evidence suggesting a connection between lee yang singularities of the magnetization of the ising model and the singularities of the effective fugacity is presented

the ising partition function zeros and deterministic approximation we study the problem of approximating the partition function of the ferromagnetic ising model with both pairwise as well as higher order interactions equivalently in graphs as well as hypergraphs our approach is based on the classical lee yang theory of phase transitions along with a new lee yang theorem for the ising model with higher order interactions and on an extension of ideas developed recently by barvinok and patel and regts that can be seen as an algorithmic realization of the lee yang theory our first result is a deterministic polynomial time approximation scheme an fptas for the partition function in bounded degree graphs that is valid over the entire range of parameters beta the interaction and lambda the external field except for the case left lambda right 1 the zero field case a polynomial time randomized approximation scheme fpras for all graphs and all beta lambda based on markov chain monte carlo simulation has long been known unlike most other deterministic approximation algorithms for problems in statistical physics and counting our algorithm does not rely on the decay of correlations property but as pointed out above on lee yang theory this approach extends to the more general setting of the ising model on hypergraphs of bounded degree and edge size where no previous algorithms even randomized were known for a wide range of parameters in order to achieve this latter extension we establish a tight version of the lee yang theorem for the ising model on hypergraphs improving a classical result of suzuki and fisher

perturbative analysis of disordered ising models close to criticality we consider a two dimensional ising model with random i i d nearest neighbor ferromagnetic couplings and no external magnetic field we show that if the probability of supercritical couplings is small enough the system admits a convergent cluster expansion with probability one the associated polymers are defined on a sequence of increasing scales in particular the convergence of the above expansion is compatible with the infinite differentiability of the free energy but does not imply its analyticity the basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder

on the limiting set of singular values of toeplitz matrices abstract this paper is devoted to the description of the limiting set of teoplitz matrices generated by functions being locally normal over qc

the two faces of nmo abstract in many present day applications in seismic processing the assumption of a homogeneous model leads to simple yet powerful approximations which also work well when heterogeneity is not negligible while the classical normal moveout nmo hyperbola assumes an effective constant velocity medium de bazelaire based on optical projections introduced an alternative way to account for heterogeneity by shifting the reference time rather than the velocity although modern multiparameter nmo descriptions usually are based on the same set of parameters we show through reparameterization that they can be divided into the same two types of approximations one assuming an effective medium the other describing the optical analogue in a medium of constant near surface velocity we provide new insights into the auxiliary medium concept and introduce a generalized osculating equation which allows for the forward and inverse transformation between the effective and the optical domain thereby providing a uni

fluctuations of the free energy in the rem and the p spin sk models we consider the random fluctuations of the free energy in the p spin version of the sherrington kirkpatrick sk model in the high temperature regime using the martingale approach of comets and neveu as used in the standard sk model combined with truncation techniques inspired by a recent paper by talagrand on the p spin version we prove that the random corrections to the free energy are on a scale n p 2 2 only and after proper rescaling converge to a standard gaussian random variable this is shown to hold for all values of the inverse temperature smaller than a critical p we also show that p 2 in 2 as p additionally we study the formal p limit of these models the random energy model here we compute the precise limit theorem for the properly rescaled partition function at all temperatures for 2 in 2 fluctuations are found at an exponentially small scale with two distinct limit laws above and below a second critical value in 2 2 for up to that value the rescaled fluctuations are gaussian while below that there are non gaussian fluctuations driven by the poisson process of the extreme values of the random energies for larger than the critical 2 in 2 the fluctuations of the logarithm of the partition function are on a scale of 1 and are expressed in terms of the poisson process of extremes at the critical temperature the partition function divided by its expectation converges to 1 2

quasi additive estimates on the hamiltonian for the one dimensional long range ising model in this work we study the problem of getting quasi additive bounds for the hamiltonian of the long range ising model when the two body interaction term decays proportionally to 1d2 0 1 we revisit the paper by cassandro et al j math phys 46 053305 2005 where they extend to the case 0 ln3ln2 1 the result of the existence of a phase transition by using a peierls argument given by frohlich and spencer commun math phys 84 87 101 1982 for 0 the main arguments of cassandro et al j math phys 46 053305 2005 are based in a quasi additive decomposition of the hamiltonian in terms of hierarchical structures called triangles and contours which are related to the original definition of contours introduced by frohlich and spencer commun math phys 84 87 101 1982 in this work we study the existence of a quasi additive decomposition of the hamiltonian in terms of the contours defined in the work of cassandro et al j math phys 46 053305 2005 the most relevant r

metastates in disordered mean field models ii the superstates we continue to investigate the size dependence of disordered mean field models with finite local spin space in more detail illustrating the concept of superstates as recently proposed by bovier and gayrard we discuss various notions of convergence for the behavior of the paths t tn t 0 1 in the thermodynamic limit n here n is the gibbs measure in the finite volume 1 n and is the disorder variable in particular we prove refined convergence statements in our concrete examples the hopfield model with finitely many patterns having continuous paths and the curie weiss random field ising model having singular paths

entropy limit theorems and variational principles for disordered lattice systems we study infinite volume limits and gibbs states of disordered lattice systems with bounded and continuous potentials our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes we find that many familiar results of invariant potentials such as large deviation theorems variational principles and equivalence of ensembles continue to hold for disordered models with suitably modified statements

on the structure of kms states of disordered systems we study the set of kms states of spin systems with random interactions this is done in the framework of operator algebras by investigating connes and borchers invariants of w dynamical systems in the case of kms states exhibiting a property of invariance with respect to the spatial translations some interesting properties emerge naturally such a situation covers kms states obtained by infinite volume limits of finite volume gibbs states that is the quenched disorder this analysis can be considered as a step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses and its connection with the breakdown of the symmetry for replicas

loop calculus for nonbinary alphabets using concepts from information geometry the bethe approximation is a well known approximation of the partition function used in statistical physics recently an equality relating the partition function and its bethe approximation was obtained for graphical models with binary variables by chertkov and chernyak in this equality the multiplicative error in the bethe approximation is represented as a weighted sum over all generalized loops in the graphical model in this paper the equality is generalized to graphical models with nonbinary alphabet using concepts from information geometry

relaxation of disordered magnets in the griffiths regime we study the relaxation to equilibrium of discrete spin systems with random finite range not necessarily ferromagnetic interactions in the griffiths regime we prove that the speed of convergence to the unique reversible gibbs measure is almost surely faster than any stretched exponential at least if the probability distribution of the interaction decays faster than exponential e g gaussian furthermore if the interac tion is uniformly bounded the average over the disorder of the time autocorrelation function goes to equilibrium as exp k log t d d 1 in d 1 in agreement with previous results obtained for the dilute ising model

curvatures and inhomogeneities an improved common reflection surface approach abstractmultiparameter stacking is an important tool to obtain a first reliable time image of the subsurface in addition it provides wavefield attributes which form the basis for many important applications the quality of the image and the attribute estimates relies heavily on the accuracy of the traveltime moveout description the commonly used hyperbolic common reflection surface crs operator reduces to the nmo hyperbola in the common midpoint gather its accuracy however depends on the curvature of the reflector under consideration the conventional multifocusing mf operator a time shifted double square root expression leads to good results for high reflector curvatures and moderate inhomogeneities of the overburden we used a new implicit crs formulation that combines the robustness of crs regarding heterogeneities with the high sensitivity to curvature of the mf approach it assumes reflectors to be locally circular and can be applied in an iterative fashion for simple but common acquisi

graded cluster expansion for lattice systems in this paper we develop a general theory which provides a unified treatment of two apparently different problems the weak gibbs property of measures arising from the application of renormalization group maps and the mixing properties of disordered lattice systems in the griffiths phase we suppose that the system satisfies a mixing condition in a subset of the lattice whose complement is sparse enough namely large regions are widely separated we then show how it is possible to construct a convergent multi scale cluster expansion

determination of wavefront attributes by differential evolution in the presence of conflicting dips abstractthe common reflection surface crs method represents a multidimensional stacking approach i e the stacking surface is determined in the midpoint and offset directions in the 2d case three attributes span the stacking surface thus requiring a three parameter search contrary to a one parameter search in the classic common midpoint stack however crs wavefront attributes use data redundancy in the midpoint direction as well which makes them very useful in several seismic applications e g data preconditioning velocity model building and migration contrary to previous works we simultaneously estimate crs attributes using differential evolution in subcubes of the 3d search space differential evolution is a global optimization technique that performs particularly well when the objective function is unknown because we apply de for each subcube we could find local maxima additionally to the global maximum therefore conflicting dips are recognized and can be used for the stack and subs

the restriction of the ising model to a layer we discuss the status of recent gibbsian descriptions of the restriction projection of the ising phases to a layer we concentrate on the projection of the two dimensional low temperature ising phases for which we prove a variational principle

phase transition in the 3d random field ising model we show that the three dimensional ising model coupled to a small random magnetic field is ordered at low temperatures this means that the lower critical dimension dl for the theory isdl 2 settling a long controversy on the subject our proof is based on an exact renormalization group rg analysis of the system this analysis is carried out in the domain wall representation of the system and it is inspired by the scaling arguments of imry and ma the rg acts in the space of ising models and in the space of random field distributions driving the former to zero temperature and the latter to zero variance

on the symmetry of the gibbs states in two dimensional lattice systems under fairly general conditions if a two dimensional classical lattice system has an internal symmetry groupg which is a compact connected lie group then all gibbs states areg invariant

eigenvalues and pseudo eigenvalues of toeplitz matrices the eigenvalues of a nonhermitian toeplitz matrix a are usually highly sensitive to perturbations having condition numbers that increase exponentially with the dimension n an equivalent statement is that the resolvent zz a of a toeplitz matrix may be much larger in norm than the eigenvalues alone would suggest exponentially large as a function of n even when z is far from the spectrum because of these facts the meaningfulness of the eigenvalues of nonhermitian toeplitz matrices for any but the most theoretical purposes should be considered suspect in many applications it is more meaningful to investigate the e pseudo eigenvalues the complex numbers z with ll zz a 11 l this paper analyzes the pseudospectra of toeplitz matrices and in particular relates them to the symbols of the matrices and thereby to the spectra of the associated toeplitz and laurent operators our results are reasonably complete in the triangular case and preliminary in the cases of nontriangular toeplitz matrices block toeplitz matrices and toeplitz like matrices with smoothly varying coefficients computed examples of pseudospectra are presented throughout and applications in numerical analysis are mentioned

loss network representation of peierls contours we present a probabilistic approach for the study of systems with exclusions in the regime traditionally studied via cluster expansion methods in this paper we focus on its application for the gases of peierls contours found in the study of the ising model at low temperatures but most of the results are general we realize the equilibrium measure as the invariant measure of a loss network process whose existence is ensured by a subcriticality condition of a dominant branching process in this regime the approach yields besides existence and uniqueness of the measure properties such as exponential space convergence and mixing and a central limit theorem the loss network converges exponentially fast to the equilibrium measure without metastable traps this convergence is faster at low temperatures where it leads to the proof of an asymptotic poisson distribution of contours our results on the mixing properties of the measure are comparable to those obtained with duplicated variables expansion used to treat systems with disorder and coupled map lattices it works in a larger region of validity than usual cluster expansion formalisms and it is not tied to the analyticity of the pressure in fact it does not lead to any kind of expansion for the latter and the properties of the equilibrium measure are obtained without resorting to combinatorial or complexanalysis techniques

griffiths singularities in diluted ising models on the cayley tree the griffiths singularities are fully exhibited for a class of diluted ferromagnetic ising models defined on the cayley tree bethe lattice for the deterministic model the lee yang circle theorem is explicitly proven for the magnetization at the origin and it is shown that in the thermodynamic limit the lee yang singularities become dense in the entire unit circle for the whole ferromagnetic phase smoothness infinite differentiability of the quenched magnetizationm at the origin with respect to the external magnetic field is also proven for convenient choices of temperature and disorder from our analysis we also conclude that the existence of metastable states is impossible for the random models under consideration

characterizations of the polynomial numerical hull of degree k six characterizations of the polynomial numerical hull of degree k are established for bounded linear operators on a hilbert space it is shown how these characterizations provide a natural distinction between interior and boundary points one of the characterizations is used to prove that the polynomial numerical hull of any fixed degree k for a toeplitz matrix whose symbol is piecewise continuous approaches all or most of that of the infinite dimensional toeplitz operator as the matrix size goes to infinity

infinite dimensional srb measures we review the basic steps leading to the construction of a sinai ruelle bowen srb measure for an infinite lattice of weakly coupled expanding circle maps and we show that this measure has exponential decay of space time correlations first using the perron frobenius operator one connects the dynamical system of coupled maps on a d dimensional lattice to an equilibrium statistical mechanical model on a lattice of dimension d 1 this lattice model is for weakly coupled maps in a high temperature phase and we use a general but very elementary method to prove exponential decay of correlations at high temperatures

taming griffiths singularities infinite differentiability of quenched correlation functions we prove infinite differentiability of the magnetization and of all quenched correlation functions for disordered spin systems at high temperature or strong magnetic field in the presence of griffiths singularities we also show uniqueness of the gibbs state and exponential decay of truncated correlation functions with probability one our results are obtained through new simple modified high temperature or low activity expansions whose convergence can be displayed by elementary probabilistic arguments our results require no assumptions on the probability distributions of the random parameters except for the obvious one of no percolation of infinite couplings and in the strong field situation for the also obvious requirement that zero magnetic fields do not percolate

dynamics at a smeared phase transition we investigate the effects of rare regions on the dynamics of ising magnets with planar defects i e disorder perfectly correlated in two dimensions in these systems the magnetic phase transition is smeared because static long range order can develop on isolated rare regions we first study an infinite range model by numerically solving local dynamic mean field equations then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean field theory in the tail region of the smeared transition the dynamics is even slower than in a conventional griffiths phase the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times

on the distribution and gap structure of lee yang zeros for the ising model periodic and aperiodic couplings in this work we present some results on the distribution of lee yang zeros for the ferromagnetic ising model on the rooted cayley tree bethe lattice assuming free boundary conditions and in the one dimensional lattice with periodic boundary conditions in the case of the cayley tree we derive the conditions that the interactions between spins must obey in order to ensure existence or absence of phase transition at finite temperature t 0 the results are first obtained for periodic interactions along the generations of the lattice then using periodic approximants we are also able to obtain results for aperiodic sequences generated by substitution rules acting on a finite alphabet the particular examples of the fibonacci and the thue morse sequences are discussed most of the results are obtained for a cayley tree with arbitrary order d we will be concerned in showing whether or not the zeros become dense in the whole unit circle of the fugacity variable regarding the one dimensional ising model we derive a general treatment for the structure of gaps regions free of lee yang zeros around the unit circle

on the ising model with random boundary condition the infinite volume limit behavior of the 2d ising model under possibly strong random boundary conditions is studied the model exhibits chaotic size dependence at low temperatures and we prove that the and phases are the only almost sure limit gibbs measures assuming that the limit is taken along a sparse enough sequence of squares in particular we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces in order to exclude mixtures as possible limit points a detailed multi scale contour analysis is performed

on the surface pressure for the edwards anderson model for the edwards anderson model we introduce an integral representation for the surface pressure per unit surface in terms of a quenched moment of the bond overlap on the surface we consider free periodic and antiperiodic boundary conditions by symmetry and prove the bounds open image in new windowopen image in new window we show moreover that at high temperatures is close to 2 4 and is close to 2 4 uniformly in the volume