Related papers: Transformations of one-dimensional Gibbs measures …

Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface…

We prove the Gibbs variational principle for the Asakura--Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a temperature-dependent area interaction. The particle size…

We consider a q-deformed version of the uniform Gibbs measure on dimers on the periodized hexagonal lattice (equivalently, on interlacing particle configurations, if vertical dimers are seen as particles) and show that it is invariant under…

We present a novel approach to establishing the variational principle for Gibbs and generalized (weak and almost) Gibbs states. Limitations of a thermodynamical formalism for generalized Gibbs states will be discussed. A new class of…

We consider Gibbs distributions on the set of permutations of $\mathbb Z^d$ associated to the Hamiltonian $H(\sigma):=\sum_{x} V(\sigma(x)-x)$, where $\sigma$ is a permutation and $V:\mathbb Z^d\to\mathbb R$ is a strictly convex potential.…

We are concerned with sets of generic points for shift-invariant measures in the countable symbolic space. We measure the sizes of the sets by the Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that the dimension of…

A rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting $\nu$-dimensional quantum anharmonic oscillators is given. The oscillators are indexed by the elements of a countable set…

We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…

We prove a metastability result for finitary microstates which are good models for a Gibbs measure for a nearest-neighbor interaction on a finitely-generated group. This is used to show that any maximal-entropy joining of two such Gibbs…

We give a detailed and refined proof of the Dobrushin-Pechersky uniqueness criterion extended to the case of Gibbs fields on general graphs and single-spin spaces, which in particular need not be locally compact. The exponential decay of…

In this paper, the well-known method of correlation equations for constructing Gibbs measures is generalized based on the concept of the transition energy field. Using the properties of transition energies, we obtain the system of…

We consider Ising-spin systems starting from an initial Gibbs measure $\nu$ and evolving under a spin-flip dynamics towards a reversible Gibbs measure $\mu\not=\nu$. Both $\nu$ and $\mu$ are assumed to have a finite-range interaction. We…

We discuss the $(1+1)$-dimensional wave maps equation with values in a compact Lie group. The corresponding Gibbs measure is given by a Brownian motion on the Lie group, which plays a central role in stochastic geometry. Our main theorem is…

We consider one-dimensional long-range spin models (usually called Dyson models), consisting of Ising ferromagnets with slowly decaying long-range pair potentials of the form $\frac{1}{|i-j|^{\alpha}}$ mainly focusing on the range of slow…

We derive thermodynamic functionals for spatially inhomogeneous magnetization on a torus in the context of an Ising spin lattice model. We calculate the corresponding free energy and pressure (by applying an appropriate external field using…

In this paper we study the decay of correlations for Gibbs measures associated to codimension one Axiom A attractors for flows. We prove that a codimension one Axiom A attractors whose strong stable foliation is $C^{1+\alpha}$ either have…

We study measures on the configuration spaces of two type particles. Gibbs measures on the such spaces are described. Main properties of corresponding relative energies densities and correlation functions are considered. In particular, we…

We provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability…

The simple derivation of the string equation of motion adopted in the nonrelativistic case is presented, paying the special attention to the effects of finite masses of bosonic fields of an Abelian Higgs model. The role of the finite mass…

We consider the i.i.d. Bernoulli field $\mu_p$ with occupation density $p \in (0,1)$ on a possibly non-regular countably infinite tree with bounded degrees. For large $p$, we show that the quasilocal Gibbs property, i.e. compatibility with…