Corner Transfer Matrix Algorithm for Classical Renormalization Group

TL;DR

This paper introduces a novel real-space renormalization group algorithm based on Baxter's corner transfer matrix for 2D classical lattice models, utilizing density matrix techniques to accurately compute thermodynamic properties and critical exponents.

Contribution

The paper presents a new RSRG method using CTM and density matrix algorithms, improving the accuracy of thermodynamic and critical exponent calculations for 2D classical models.

Findings

Accurately evaluated thermodynamic functions.

Precisely determined critical exponents.

Validated method on Potts models.

Abstract

We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group transformation according to White's density matrix algorithm, so that variational free energies are minimized within a restricted degree of freedom m. As a consequence of the renormalization, spin variables on each corner of CTM are replaced by a m-state block spin variable. It is shown that the thermodynamic functions and critical exponents of the q = 2, 3 Potts models can be precisely evaluated by use of the renormalization group method.