Quantum approach to nucleation times of kinetic Ising ferromagnets

TL;DR

This paper investigates the low-temperature nucleation times in kinetic Ising ferromagnets under finite magnetic fields using quantum spin representations, providing both numerical and analytical insights across various lattice types.

Contribution

It introduces a quantum spin framework to analyze nucleation times in Ising models, extending previous methods to different lattice geometries and dynamic modifications.

Findings

Relaxation times correlate with nucleation lifetimes.

Analytical and numerical methods agree on low-temperature limits.

Applicable to square, triangular, and honeycomb lattices.

Abstract

Low temperature dynamics of Ising ferromagnets under finite magnetic fields are studied in terms of quantum spin representations of stochastic evolution operators. These are constructed for the Glauber dynamic as well as for a modification of this latter, introduced by K. Park {\it et al.} in Phys. Rev. Lett. {\bf 92}, 015701 (2004). In both cases the relaxation time after a field quench is evaluated both numerically and analytically using the spectrum gap of the corresponding operators. The numerical work employs standard recursive techniques following a symmetrization of the evolution operator accomplished by a non-unitary spin rotation. The analytical approach uses low temperature limits to identify dominant terms in the eigenvalue problem. It is argued that the relaxation times already provide a measure of actual nucleation lifetimes under finite fields. The approach is applied to square, triangular and honeycomb lattices.