Mean Field Renormalization Group for the Boundary Magnetization of Strip Clusters

TL;DR

This paper introduces a mean field renormalization group method based on a transfer matrix approximation that accurately predicts critical points and boundary magnetization in 2D Ising models, aligning well with exact results.

Contribution

The authors develop a new mean field renormalization group approach that precisely determines critical points and boundary magnetization, improving understanding of finite size scaling in 2D models.

Findings

Exact critical points for 2D Ising models obtained

Critical exponents closely match exact values

Method clarifies strengths and limitations of mean field RG

Abstract

We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that this approximation yields not only the exact critical point, but also the exact boundary magnetization of a semi--infinite Ising model, independent of the size of the strips used. Then we develop a new mean field renormalization group strategy based on this approximation and make connections with finite size scaling. Applying our strategy to the quadratic Ising and three--state Potts models we obtain results for the critical exponents which are in excellent agreement with the exact ones. In this way we also clarify some advantages and limitations of the mean field renormalization group approach.