A Density Matrix Algorithm for 3D Classical Models

TL;DR

This paper extends the density matrix renormalization group method to three-dimensional classical models, enabling more effective analysis of complex 3D systems like the Ising model.

Contribution

It introduces a generalized 3D density matrix algorithm based on corner transfer matrices, expanding the applicability of existing 2D methods.

Findings

Successfully applied to 3D Ising model with m=2

Demonstrates feasibility of 3D density matrix approach

Provides a foundation for future 3D model analysis

Abstract

We generalize the corner transfer matrix renormalization group, which consists of White's density matrix algorithm and Baxter's method of the corner transfer matrix, to three dimensional (3D) classical models. The renormalization group transformation is obtained through the diagonalization of density matrices for a cubic cluster. A trial application for 3D Ising model with m=2 is shown as the simplest case.