Monte Carlo Renormalization Group for Systems with Quenched Disorder

TL;DR

This paper introduces a variational Monte Carlo renormalization group method tailored for quenched disordered systems, enabling analysis of critical behavior and coupling distributions with reduced computational effort.

Contribution

It extends a variational real space renormalization scheme to disordered systems, allowing for efficient computation of critical exponents and coupling distributions.

Findings

Successfully applied to 2D dilute Ising model

Effective in quantum and classical disordered systems

Reduces Monte Carlo relaxation time significantly

Abstract

We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two and three dimensional lattices.