This is a tutorial review on the Potts model aimed at bringing out in an organized fashion the
essential and important properties of the standard Potts model. Emphasis is placed on exact …

This book was conceived as a slim monograph, but grew to its present size as I attempted to
set down an account of two-dimensional lattice models in statistical mechanics, and how …

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 …

A theorem of J. Alexander [1] asserts that any tame oriented link in 3-space may be
represented by a pair (b, n), where b is an element of the n-string braid group Bn. The link L …

By studying representations of the braid group satisfying a certain quadratic relation we
obtain a polynomial invariant in two variables for oriented links. It is expressed using a trace …

Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics.
This book provides, for the first time, a comprehensive collection of their properties and …

This review addresses recent developments in non-equilibrium statistical physics. Focusing
on phase transitions from fluctuating phases into absorbing states, the universality class of …

The random-cluster model is defined as a model for phase transitions and other phenomena
in lattice systems, or more generally in systems with a graph structure. The model is …

We examine some current ideas concerning the differences between covalent random
networks with high and low average coordination. These ideas can be made rigorous by …

Entropy is a concept which appears in several fields and it is in the center of interest both in
mathematical and physical subjects, sometimes even at other places, for example in …