Publications
89 results found
Guionnet A, Zegarlinski B, 1996, Decay to equilibrium in random spin systems on a lattice, Communications in Mathematical Physics, Vol: 181, Pages: 703-732, ISSN: 0010-3616
STROOCK D, ZEGARLINSKI B, 1995, ON THE ERGODIC PROPERTIES OF GLAUBER DYNAMICS, JOURNAL OF STATISTICAL PHYSICS, Vol: 81, Pages: 1007-1019, ISSN: 0022-4715
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- Citations: 15
VANENTER A, ZEGARLINSKI B, 1995, A REMARK ON DIFFERENTIABILITY OF THE PRESSURE FUNCTIONAL, REVIEWS IN MATHEMATICAL PHYSICS, Vol: 7, Pages: 959-977, ISSN: 0129-055X
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- Citations: 2
Zegarlinski B, 1995, Ergodicity of Markov semigroups on infinite dimensional spaces, Berlin 30, international conference on dirichlet forms and stochastic processes OCT 25-31, 1993 BEIJING, PEOPLES R CHINA, Publisher: Walter de Gruyter, Pages: 405-415
ZEGARLINSKI B, 1994, STRONG DECAY TO EQUILIBRIUM IN ONE-DIMENSIONAL RANDOM SPIN SYSTEMS, JOURNAL OF STATISTICAL PHYSICS, Vol: 77, Pages: 717-732, ISSN: 0022-4715
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- Citations: 11
Albeverio S, Tirozzi B, Zegarlinski B, 1992, Rigorous results for the free energy in the Hopfield model, Communications in Mathematical Physics, Vol: 150, Pages: 337-373, ISSN: 0010-3616
We prove that the free energy of the Hopfield model with a finite number of patterns can be represented in terms of an asymptotic series expansion in inverse powers of the neurons number. The series is Borel summable for large temperatures. We also establish mathematically some other interesting properties, partly used before in a seminal paper by Amit, Gutfreund and Sompolinsky. © 1992 Springer-Verlag.
Stroock DW, Zegarlinski B, 1992, The logarithmic sobolev inequality for discrete spin systems on a lattice, Communications in Mathematical Physics, Vol: 149, Pages: 175-193, ISSN: 0010-3616
For finite range lattice gases with a finite spin space, it is shown that the Dobrushin-Shlosman mixing condition is equivalent to the existence of a logarithmic Sobolev inequality for the associated (unique) Gibbs state. In addition, implications of these considerations for the ergodic properties of the corresponding Glauber dynamics are examined. © 1992 Springer-Verlag.
Stroock DW, Zegarlinski B, 1992, The logarithmic Sobolev inequality for continuous spin systems on a lattice, Journal of Functional Analysis, Vol: 104, Pages: 299-326, ISSN: 0022-1236
In this article, we give (cf. Theorem 1.6) a sufficient condition on a local specification for the associated Gibbs state to satisfy a logarithmic Sobolev inequality. In the final section (cf. Theorem 3.10) we relate our condition to the type of mixing condition introduced by Dobrushin and Shlosman in connection with their work on complete analyticity. © 1992.
Albeverio S, Hohler EGB, Zegarlinski B, 1992, Ferromagneticity of simplicial fields on two-dimensional compact manifolds, Journal of Mathematical Physics, Vol: 33, Pages: 2808-2818, ISSN: 0022-2488
Smooth triangulations of a compact smooth connected two-dimensional Riemannian manifold M are considered. The q-simplicial fields are defined with values in the space of q-cochains and a natural Gaussian measure is defined giving their distribution, with covariance defined essentially in terms of the combinatorial Laplacian Δc. In the continuum limit this measure for q=0 is the free quantum field measure over M. In this case it is shown that for a certain collection of triangulations there exists a sequence of subdivisions of each triangulation such that the corresponding measure is ferromagnetic. It is also shown that for sufficiently fine subdivisions - Δ+m2double-struck I sign, m>0 has nonpositive off-diagonal elements. The proofs are obtained by a result on triangulations by simplexes with acute angles. It is also proven that the probability measures describing quantum fields on M with polynomial, trigonometric, or exponential interactions satisfy FKG inequalities. © 1992 American Institute of Physics.
Zegarlinski B, Stroock DW, 1992, The equivalence of the logarithmic Sobolev inequality and the Dobrushin - Shlosman mixing condition., Commun. Math. Phys., Vol: 144, Pages: 303-323
Zegarlinski B, 1992, Dobrushin uniqueness theorem and logarithmic Sobolev inequalities, Journal of Functional Analysis, Vol: 105, Pages: 77-111
Fröhlich J, Zegarlinski B, 1991, The phase transition in the discrete Gaussian chain with 1/r<sup>2</sup> interaction energy, Journal of Statistical Physics, Vol: 63, Pages: 455-485, ISSN: 0022-4715
We exhibit a phase transition from a rough high-temperature phase to a rigid (localized) low-temperature phase in the discrete Gaussian chain with 1/r2 interaction energy. This transition is related to a localization transition in the ground state for a quantum mechanical particle in a one-dimensional periodic potential, coupled to quantum 1/f noise. © 1991 Plenum Publishing Corporation.
Zegarlinski B, 1991, Interactions and pressure functionals for disordered lattice systems, Communications in Mathematical Physics, Vol: 139, Pages: 305-339, ISSN: 0010-3616
The purpose of this paper is to provide a theoretical framework for disordered spin systems on a lattice, similar to that of classical statistical mechanics in the sense of Ruelle [Ru]. We prove the existence of a continuous pressure functional on a large Banach space of random interactions (highly generalizing the classical one) and formulate an analog of the variational principle. © 1991, Springer-Verlag. All rights reserved.
Zegarlinski B, 1990, On log-Sobolev inequalities for infinite lattice systems, Letters in Mathematical Physics, Vol: 20, Pages: 173-182, ISSN: 0377-9017
For a system on an infinite lattice, we show that a Gibbs measure μ for a smooth local specification ℰ={EΛ}Λ∈ℱ satisfying the Dobrushin uniqueness theorem also satisfies log-Sobolev inequality, provided it is satisfied for one-dimensional measures El∈ℰ. © 1990 Kluwer Academic Publishers.
Albeverio S, Zegarlinski B, 1990, Construction of convergent simplicial approximations of quantum fields on Riemannian manifolds, Communications in Mathematical Physics, Vol: 132, Pages: 39-71, ISSN: 0010-3616
We construct simplicial approximations of random fields on Riemannian manifolds of dimension d. We prove convergence of the fields to the continuum limit, for arbitrary d in the Gaussian case and for d=2 in the non-Gaussian case. In particular we obtain convergence of the simplicial approximation to the continuum limit for quantum fields on Riemannian manifolds with exponential interaction. © 1990 Springer-Verlag.
Zegarlinski B, 1990, On equivalence of spin and field pictures of lattice systems, Journal of Statistical Physics, Vol: 59, Pages: 1511-1530, ISSN: 0022-4715
We investigate the spin and field systems on a lattice connected by the Kac-Siegert transform. It is shown that the structures of corresponding theories are equivalent (in the sense of isomorphy of space of Gibbs states and order parameters). Using the idea of equivalence of spin and field pictures, we exhibit a class of lattice systems possessing infinitely uncountably many ground states. The systems of this type with infinite-range, slow-decaying interactions are expected to have a spin-glass phase transition. © 1990 Plenum Publishing Corporation.
Zegarliński B, 1990, Log-Sobolev inequalities for infinite one-dimensional lattice systems, Communications in Mathematical Physics, Vol: 133, Pages: 147-162
Fröhlich J, Zegarlinski B, 1989, Spin glasses and other lattice systems with long range interactions, Communications In Mathematical Physics, Vol: 120, Pages: 665-688, ISSN: 0010-3616
We study classical lattice systems, in particular real spin glasses with Ruderman-Kittel interactions and dipole gases, with interactions of very long (non-summable) range but variable sign. Using the Kac-Siegert representation of such systems and Brascamp-Lieb inequalities we are able to establish detailed properties of the high-temperature phase, such as decay of connected correlations, for these systems. © 1989 Springer-Verlag.
Albeverio S, Høegh-Krohn R, Zegarlinski B, 1989, Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions, Communications in Mathematical Physics, Vol: 123, Pages: 377-424, ISSN: 0010-3616
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 φ{symbol}24 (also in the case of non-uniqueness), and global Markov property for weak coupling φ{symbol}24 (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. © 1989 Springer-Verlag.
Albeverio S, Høegh-Krohn R, Zegarlinski B, 1989, Uniqueness of Gibbs states for general P(ϕ)2-weak coupling models by cluster expansion, Communications in Mathematical Physics, Vol: 121, Pages: 683-697, ISSN: 0010-3616
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. © 1989 Springer-Verlag.
Fröhlich J, Zegarlinski B, 1987, Some comments on the Sherrington-Kirkpatrick model of spin glasses, Communications in Mathematical Physics, Vol: 112, Pages: 553-566, ISSN: 0010-3616
In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated explicitly for the SK model, and uniform bounds on quenched susceptibilities are established. It is also shown that, at high temperatures, mean-field spin glasses are limits of short-range spin glasses, as the range of the interactions tends to infinity. © 1987 Springer-Verlag.
Zegarlinski B, 1987, Spin glasses with long-range interaction at high temperatures, Journal of Statistical Physics, Vol: 47, Pages: 911-930, ISSN: 0022-4715
We study the Ising and N-vector spin glasses with exchange couplings J=(Jij;i, jεZd), which are independent random variables with EJij=0 and EJnij≤γnn!|i-j|-nαd, for nεℕ, some finite constant γ>0, and α>1/2. For sufficiently small β, we show that for E-a.a. J there is a weakly unique, extremal, infinite-volume Gibbs measure μβJ for which the expectation of a single (component of) spin vanishes and which has the cluster property in L2(E) with the same decay as interaction. This work is based on results and methods of Fröhlich and Zegarlinski. © 1987 Plenum Publishing Corporation.
Fröhlich J, Zegarlinski B, 1987, The high-temperature phase of long-range spin glasses, Communications in Mathematical Physics, Vol: 110, Pages: 121-155, ISSN: 0010-3616
We analyze the high-temperature phase of long-range Ising- and N-vector spin glasses with exchange couplings {Jij}, i, j∈Zd, which are independent random variables with Jij=0 and {Mathematical expression} is a finite constant and α>1/2. We show that, for sufficiently high temperatures, the equilibrium state in the thermodynamic limit is (weakly) unique, and the quenched average of the square of connected correlations 〈σA; σB〉β decays like (A, B)-αd, despite of Griffiths singularities and the non-summable range of Jij (for {Mathematical expression}). © 1987 Springer-Verlag.
Zegarliński B, 1987, Extremality and the global Markov property. I. The Euclidean fields on a lattice, Journal of Multivariate Analysis, Vol: 21, Pages: 158-167, ISSN: 0047-259X
We give general conditions for extremality and the global Markov property of Gibbs measures for an attractive Markov specification. As a special case we prove the global Markov property for the FKG-maximal Gibbs measures μ±, which give models of Euclidean Field Theory on the lattice. © 1987.
Zegarliński B, 1986, The Gibbs measures and partial differential equations - I. Ideas and local aspects, Communications in Mathematical Physics, Vol: 107, Pages: 411-429, ISSN: 0010-3616
We investigate the connections of the Gibbs measures, which appear in Euclidean Field Theory, and the corresponding partial differential equations of Classical Euclidean Field Theory. © 1986 Springer-Verlag.
Fröhlich J, Zegarlinski B, 1986, The disordered phase of long-range ising spin glasses, EPL, Vol: 2, Pages: 53-60, ISSN: 0295-5075
We study the high-temperature phase of Ising spin glasses with exchange couplings (Jij), i, j in Zdwhich are independent random variables with (Formula presented.) and (Formula presented.), p = 2, 3, …, where γ is a finite constant, and (Formula presented.). For sufficiently small β, we show that, despite Griffiths singularities and of the very long range of Jijthe Edwards-Anderson order parameter vanishes, and the quenched average of the square of the connected correlation (Formula presented.) decays like (Formula presented.). © 1986 IOP Publishing Ltd.
Zegarliński B, 1986, Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures, Journal of Statistical Physics, Vol: 43, Pages: 687-705, ISSN: 0022-4715
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. © 1986 Plenum Publishing Corporation.
Zegarliński B, 1984, Uniqueness and the global Markov property for Euclidean fields: The case of general exponential interaction, Communications in Mathematical Physics, Vol: 96, Pages: 195-221, ISSN: 0010-3616
The uniqueness and the global Markov property for the regular Gibbs measure corresponding to the interaction {Mathematical expression} [for λ>0, dρ{variant}(α) a probability measure with support in {Mathematical expression}] is proved. © 1984 Springer-Verlag.
Gielerak R, Zegarliński B, 1984, Uniqueness and Global almost Markov property for regularized Yukawa gases, Fortschritte der Physik, Vol: 32, Pages: 1-24, ISSN: 0015-8208
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- Citations: 4
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