7,502 research outputs found
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 --state Potts model at (inverse)
temperature , in presence of an external magnetic field . 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 coincides with the line of first
order phase transition for small fields when 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 equals to the leading order, as goes to
where 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
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