Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets

TL;DR

This study examines the slow zero-temperature relaxation dynamics of three-dimensional Ising ferromagnets, revealing exponential relaxation times, persistent blinking spins, and complex domain structures with many holes.

Contribution

It provides new insights into the long-time behavior and complex domain topologies of 3D Ising ferromagnets after zero-temperature quenches.

Findings

Relaxation time scales exponentially with system size, tau ~ exp(L^2).

Presence of persistent 'blinker' spins that flip indefinitely without energy change.

Domains exhibit complex, highly interconnected structures with many holes, characterized by a genus scaling as L^1.7.

Abstract

We investigate the properties of the Ising-Glauber model on a periodic cubic lattice of linear dimension L after a quench to zero temperature. The resulting evolution is extremely slow, with long periods of wandering on constant energy plateaux, punctuated by occasional energy-decreasing spin-flip events. The characteristic time scale tau for this relaxation grows exponentially with the system size; we provide a heuristic and numerical evidence that tau exp(L^2). For all but the smallest-size systems, the long-time state is almost never static. Instead the system contains a small number of "blinker" spins that continue to flip forever with no energy cost. Thus the system wanders ad infinitum on a connected set of equal-energy blinker states. These states are composed of two topologically complex interwoven domains of opposite phases. The average genus g_L of the domains scales as L^gamma, with gamma~1.7; thus domains typically have many holes, leading to a "plumber's nightmare" geometry.