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Zero-temperature relaxation of three-dimensional Ising ferromagnets

J. Olejarz, P. L. Krapivsky, and S. Redner

  • Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA

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Phys. Rev. E 83, 051104 – Published 2 May, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.051104

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 plateaus, punctuated by occasional energy-decreasing spin-flip 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(L2). 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 gL of the domains scales as Lγ, with γ≈1.7; thus, domains typically have many holes, leading to a “plumber’s nightmare” geometry.

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      Phys. Rev. E 83, 051104– Published 2 May, 2011
      • Received 13 January 2011
      Article part of CHORUS

      ©2011 American Physical Society

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