Across Dimensions: Two- and Three-Dimensional Phase Transitions from the Iterative Renormalization-Group Theory of Chains

TL;DR

This paper introduces a novel iterative renormalization-group approach that couples exactly solved Ising chains to model sharp phase transitions in two and three dimensions, capturing crossover phenomena.

Contribution

It presents a new flexible method that couples one-dimensional chains to simulate higher-dimensional phase transitions using renormalization-group theory.

Findings

Successfully models sharp phase transitions in 2D and 3D.

Captures crossover from temperature-like to field-like RG flows.

Method is adaptable to various systems.

Abstract

Sharp two- and three-dimensional phase transitional magnetization curves are obtained by an iterative renormalization-group coupling of Ising chains, which are solved exactly. The chains by themselves do not have a phase transition or non-zero magnetization, but the method reflects crossover from temperature-like to field-like renormalization-group flows as the mechanism for the higher-dimensional phase transitions. The magnetization of each chain acts, via the interaction constant, as a magnetic field on its neighboring chains, thus entering its renormalization-group calculation. The method is highly flexible for wide application.