Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-01-04
Phys. Rev. E 83, 051104 (2011)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 20 figure, 4 tables, revtex4-1 format
Scientific paper
10.1103/PhysRevE.83.051104
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.
Krapivsky Paul. L.
Olejarz Jason
Redner Sid
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