19,628 research outputs found
Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart
We consider an Ising competitive model defined over a triangular Husimi tree
where loops, responsible for an explicit frustration, are even allowed. After a
critical analysis of the phase diagram, in which a ``gas of non interacting
dimers (or spin liquid) - ferro or antiferromagnetic ordered state'' transition
is recognized in the frustrated regions, we introduce the disorder for studying
the spin glass version of the model: the triangular +/- J model. We find out
that, for any finite value of the averaged couplings, the model exhibits always
a phase transition, even in the frustrated regions, where the transition turns
out to be a glassy transition. The analysis of the random model is done by
applying a recently proposed method which allows to derive the upper phase
boundary of a random model through a mapping with a corresponding non random
one.Comment: 19 pages, 11 figures; content change
A hard-sphere model on generalized Bethe lattices: Statics
We analyze the phase diagram of a model of hard spheres of chemical radius
one, which is defined over a generalized Bethe lattice containing short loops.
We find a liquid, two different crystalline, a glassy and an unusual
crystalline glassy phase. Special attention is also paid to the close-packing
limit in the glassy phase. All analytical results are cross-checked by
numerical Monte-Carlo simulations.Comment: 24 pages, revised versio
Statistical mechanics on isoradial graphs
Isoradial graphs are a natural generalization of regular graphs which give,
for many models of statistical mechanics, the right framework for studying
models at criticality. In this survey paper, we first explain how isoradial
graphs naturally arise in two approaches used by physicists: transfer matrices
and conformal field theory. This leads us to the fact that isoradial graphs
provide a natural setting for discrete complex analysis, to which we dedicate
one section. Then, we give an overview of explicit results obtained for
different models of statistical mechanics defined on such graphs: the critical
dimer model when the underlying graph is bipartite, the 2-dimensional critical
Ising model, random walk and spanning trees and the q-state Potts model.Comment: 22 page
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