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

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.

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• Comment on `Series expansions from the corner transfer matrix renormalization group method: the hard-squares model'
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• Accurate lower bounds on two-dimensional constraint capacities from corner transfer matrices
• Lattice and PT symmetries in tensor-network renormalization group: Case study of a hard-square lattice gas model
• Upper bounds on the growth rates of hard squares and related models via corner transfer matrices