Universal Dynamics of Independent Critical Relaxation Modes

TL;DR

This paper investigates the universal behavior of relaxation modes in critical systems, developing a variational scheme to accurately compute eigenvalues and correlation times, revealing universal spectra across models in the 2D Ising class.

Contribution

It introduces a variational approach to optimize independent relaxation modes and reduces statistical errors in eigenvalue computations for critical phenomena.

Findings

Eigenvalues and correlation times are universal up to a single non-universal scale.

The developed scheme improves accuracy of relaxation mode spectra.

Results apply to models in the 2D Ising universality class.

Abstract

Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme is developed to optimize variational approximants of progressively rapid, independent relaxation modes. These approximants are used to reduce the variance of results obtained by means of an adaptation of a quantum Monte Carlo method to compute eigenvalues subject to errors predominantly of statistical nature. The resulting spectra and correlation times are found to be universal up to a single, non-universal time scale for each model.