Real-space renormalization group for the random-field Ising model

TL;DR

This paper applies real-space renormalization group techniques to analyze the critical behavior of the three-dimensional random-field Ising model, identifying a zero-temperature critical fixed point and universal crossover phenomena.

Contribution

It introduces a two-parameter RG approach to study the critical properties and crossover behavior of the 3D random-field Ising model, including scaling fields and exponents.

Findings

Transition controlled by a zero-temperature disordered fixed point

Universal crossover from pure Ising critical point

Distribution of barrier heights analyzed

Abstract

We present real--space renormalization group (RG) calculations of the critical properties of the random--field Ising model on a cubic lattice in three dimensions. We calculate the RG flows in a two--parameter truncation of the Hamiltonian space. As predicted, the transition at finite randomness is controlled by a zero temperature, disordered critical fixed point, and we exhibit the universal crossover trajectory from the pure Ising critical point. We extract scaling fields and critical exponents, and study the distribution of barrier heights between states as a function of length scale.