Quantum approach to nucleation times of kinetic Ising ferromagnets

Details Quantum approach to nucleation times of kinetic Ising ferromagnets Quantum approach to nucleation times of kinetic Ising ferromagnets

2005-01-14

arxiv.org/abs/cond-mat/0501351v1

Phys. Rev. E 71, 066104 (2005)

Physics

Condensed Matter

Statistical Mechanics

14 pages, 6 figures

Scientific paper

10.1103/PhysRevE.71.066104

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.

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