Corner transfer matrices in statistical mechanics

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.

18 pages, 4 figures, for Proceedings of Conference on Symmetries and Integrability of Difference Equations. (SIDE VII), Melbourne, July 2006

References in corpus (3)

• Planar lattice gases with nearest-neighbour exclusion
• Difference equations for the correlation functions of the eight vertex model
• Derivation of the order parameter of the chiral Potts model

Cited by in corpus (9)

• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Variational approach to the scaling function of the 2D Ising model in a magnetic field
• Random insights into the complexity of two-dimensional tensor network calculations
• Integrability in anyonic quantum spin chains via a composite height model
• Corner Transfer Matrix Approach to the Yang-Lee Singularity in the 2D Ising Model in a magnetic field
• New symmetries of the chiral Potts model
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Local height probabilities in a composite Andrews-Baxter-Forrester model