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 and rigorous results, but other aspects of the problem are also described to achieve a unified perspective. Topics reviewed include the mean-field theory, duality relations, series expansions, critical properties, experimental realizations, and the relationship of the Potts model with other lattice-statistical problems.

The Potts model

It is shown that the two-dimensional q-component Potts model is equivalent to a staggered ice-type model. It is deduced that the model has a first-order phase transition for q>4, and a higher-order transition for q<or=4. The free energy and latent heat at the transition are calculated.

https://iopscience.iop.org/article/10.1088/0022-3719/6/23/005/pdf

Potts model at the critical temperature

Conformal invariance, the XXZ chain and the operator content of two-dimensional critical systems

Correlation functions on the critical lines of the Baxter and Ashkin-Teller models☆

We investigate the critical behaviour of the two-dimensional, q-state Potts model, using finite-size scaling and transfer matrix methods. For the continuous transition range (0 These results for continuous q were obtained from a transfer matrix constructed for a generalized Whitney polynomial representing the Potts models. An effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed.

Critical behaviour of the two-dimensional Potts model with a continuous number of states; A finite size scaling analysis

Dual transformations in many‐component Ising models in two dimensions on a square lattice are studied. The models considered include those of Ashkin and Teller and of Potts. In certain cases the dual transformation is a relation between the partition function of a lattice at high and low temperatures and can be used to determine a unique critical temperature if one exists. Dual transformations are considered both from a topological and an algebraic point of view. The topological arguments are a natural extension of those used by Onsager for the 2‐component Ising model. The transfer matrices for these models are constructed, and it is shown how the dual transformation arises in this formulation of the problem. The algebras generated by these models are investigated and provide a generalization of the spinor algebra introduced by Kaufman in the 2‐component Ising model.

L. Mittag

Papers

Dual Transformations in Many‐Component Ising Models