Zerotemperature relaxation of threedimensional Ising ferromagnets
Abstract
We investigate the properties of the IsingGlauber 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 plateaus, punctuated by occasional energydecreasing spinflip events. The characteristic time scale τ for this relaxation grows exponentially with the system size; we provide a heuristic and numerical evidence that τ~exp(L^{2}). For all but the smallestsize systems, the longtime 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 equalenergy 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^{γ}, with γ≈1.7; thus, domains typically have many holes, leading to a “plumber’s nightmare” geometry.
 Publication:

Physical Review E
 Pub Date:
 May 2011
 DOI:
 10.1103/PhysRevE.83.051104
 arXiv:
 arXiv:1101.0762
 Bibcode:
 2011PhRvE..83e1104O
 Keywords:

 05.50.+q;
 64.60.My;
 75.40.Gb;
 05.40.a;
 Lattice theory and statistics;
 Metastable phases;
 Dynamic properties;
 Fluctuation phenomena random processes noise and Brownian motion;
 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages, 20 figure, 4 tables, revtex41 format