Non-universal disordered Glauber dynamics

TL;DR

This paper investigates how disorder affects the relaxation dynamics in one-dimensional Glauber models, revealing non-universal and disorder-dependent dynamic exponents through numerical analysis.

Contribution

It introduces a fermionic Hamiltonian approach to analyze disordered Glauber dynamics and characterizes the non-universal dynamic exponents under different disorder types.

Findings

Binary disorder leads to non-universal exponents similar to dimerized chains.

Gaussian disorder results in non-universal, sub-diffusive exponents below a critical variance.

Above the critical variance, relaxation times grow as a stretched exponential of the correlation length.

Abstract

We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the non-universal values of those of plain dimerized chains. In the second situation their values are still non-universal and sub-diffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.