On the Surface Tensions of Binary Mixtures

For binary mixtures with fixed concentrations of the species, various relationships between the surface tensions and the concentrations are briefly reviewed

A manifold of pure Gibbs states of the Ising model on a Cayley tree

We study the Ising model on a Cayley tree. A wide class of new Gibbs states is exhibited

On the Kert\'esz line: Some rigorous bounds

We study the Kert\'esz line of the $q$--state Potts model at (inverse) temperature $\beta$, in presence of an external magnetic field $h$. This line separates two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin-Kasteleyn representation of the model. It is known that the Kert\'esz line $h_K (\beta)$ coincides with the line of first order phase transition for small fields when $q$ is large enough. Here we prove that the first order phase transition implies a jump in the density of the infinite cluster, hence the Kert\'esz line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that $h_K (\beta)$ equals $\log (q - 1) - \log (\beta - \beta_p)$ to the leading order, as $\beta$ goes to $\beta_p = - \log (1 - p_c)$ where $p_c$ is the threshold for bond percolation.Comment: 11 pages, 1 figur

Surface transitions of the semi-infinite Potts model I: the high bulk temperature regime

We propose a rigorous approach of Semi-Infinite lattice systems illustrated with the study of surface transitions of the semi-infinite Potts model

A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane

In this paper we construct many `new' Gibbs states of the Ising model on the Lobachevsky plane, the millefeuilles. Unlike the usual states on the integer lattices, our foliated states have infinitely many interfaces. The interfaces are rigid and fill the Lobachevsky plane with positive density.Comment: 25 pages, 7 figure

On the Statistical Mechanics and Surface Tensions of Binary Mixtures

Within a lattice model describing a binary mixture with fixed concentrations of the species we discuss the relation-ship between the surface tension of the mixture and the concentrations

Glassy states: the free Ising model on a tree

We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The tail observable showing that the free state is not extremal is related to the Edwards-Anderson parameter, measuring the variance of the (random) magnetization obtained from drawing boundary conditions from the free state