Series expansions from the corner transfer matrix renormalization group method: the hard squares model

TL;DR

This paper adapts the corner transfer matrix renormalization group method to derive series expansions for the hard squares model, calculating 92 terms of its partition function and analyzing the series' properties.

Contribution

It introduces a novel application of the CTMRG method for generating series expansions, extending its use from numerical calculations to analytical series derivation.

Findings

Calculated 92 terms of the partition function for the hard squares model.

Analyzed the series to assess the method's growth rate and properties.

Confirmed the efficiency of the adapted method for series generation.

Abstract

The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It originates from Baxter's corner transfer matrix equations and method, and was developed by Nishino and Okunishi in 1996. In this paper, we review and adapt this method, previously used for numerical calculations, to derive series expansions. We use this to calculate 92 terms of the partition function of the hard squares model. We also examine the claim that the method is subexponential in the number of generated terms and briefly analyse the resulting series.