Corner transfer matrices in statistical mechanics

TL;DR

This paper reviews the use of corner transfer matrices in 2D statistical mechanics, highlighting their effectiveness in series expansions and order parameter calculations, while also discussing their limitations with the chiral Potts model.

Contribution

It provides a comprehensive review of corner transfer matrices, explaining their successes and limitations in analyzing two-dimensional models in statistical mechanics.

Findings

Effective for series expansions of unsolved models

Useful for calculating order parameters of solved models

Fails to determine the order parameter of the chiral Potts model

Abstract

Corner transfer matrices are a useful tool in the statistical mechanics of simple two-dimensinal models. They can be very effective way of obtaining series expansions of unsolved models, and of calculating the order parameters of solved ones. Here we review these features and discuss the reason why the method fails to give the order parameter of the chiral Potts model.