ﻻ يوجد ملخص باللغة العربية
We consider Dyson models, Ising models with slow polynomial decay, at low temperature and show that its Gibbs measures deep in the phase transition region are not $g$-measures. The main ingredient in the proof is the occurrence of an entropic repulsion effect, which follows from the mesoscopic stability of a (single-point) interface for these long-range models in the phase transition region.
We study the decimation to a sublattice of half the sites, of the one-dimensional Dyson-Ising ferromagnet with slowly decaying long-range pair interactions of the form $frac{1}{{|i-j|}^{alpha}}$, in the phase transition region (1< $alpha leq$ 2, and
In this paper, we study the product of two complex Ginibre matrices and the loop equations satisfied by their resolvents (i.e. the Stieltjes transform of the correlation functions). We obtain using Schwinger-Dyson equation (SDE) techniques the genera
We construct for the first time examples of non-frustrated, two-body, infinite-range, one-dimensional classical lattice-gas models without periodic ground-state configurations. Ground-state configurations of our models are Sturmian sequences defined
In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for a large c
We discuss what ground states for generic interactions look like. We note that a recent result, due to Morris, implies that the behaviour of ground-state measures for generic interactions is similar to that of generic measures. In particular, it foll