This article reviews, from a very personal point of view, the origins and the early work on
transitions driven by topological defects such as vortices in the two dimensional planar rotor …

I give a highly selective overview of the way statistical mechanics explains the microscopic
origins of the time-asymmetric evolution of macroscopic systems towards equilibrium and of …

Suppose we immerse a large porous stone in a bucket of water. What is the probability that
the centre of the stone is wetted? In formulating a simple stochastic model for such a …

The “classical” random graph models, in particular G (n, p), are “homogeneous,” in the
sense that the degrees (for example) tend to be concentrated around a typical value. Many …

We give a simple explanation of the Swendsen-Wang algorithm for Potts models in terms of
a joint model of Potts spin variables interacting with bond occupation variables. We then …

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and
prove some rigorous theorems on the regularity properties and possible pathologies of the …

A scaling theory for the long-range to short-range crossover and an infrared duality -
IOPscience Skip to content IOP Science home Accessibility Help Search Journals Journals …

We present the results of extensive Monte Carlo simulations of Ising models with
algebraically decaying ferromagnetic interactions in the regime where classical critical …

Phase transitions are a central theme of statistical mechanics, and of probability more
generally. Lattice spin models represent a general paradigm for phase transitions in finite …

Publisher Summary This chapter discusses the random geometry of equilibrium phases.
Percolation will come into play here on various levels. Its concepts like clusters, open paths …