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Slow dynamics in 3D ± J Heisenberg spin glass; Monte Carlo analysis of auto-correlation functions of individual spins

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  • Takayama, H.
  • Yoshino, H.

Abstract

Slow dynamics in the 3D ± J Heisenberg spin glass is investigated by the Monte Carlo simulation, in which auto-correlation functions qi(t) of all individual spins in the system are evaluated. The distribution of relaxation times, τi, is extracted from qi(t). The forms of the log(τi) distribution obtained reveal that slow dynamics in this system at relatively low temperatures (T ⪅ 0.6J) is nothing but the critical slowing down associated with the T = 0 phase transition. The two decay forms of the total auto-correlation function q(t) (=N−1Σiqi(t),N being the number of spins in the system) proposed previously, i.e. the logarithmic decay and the exponential one multiplied by an argebraic factor, are understood as characteristic features of the phenomenon in different ranges of the observation time.

Suggested Citation

  • Takayama, H. & Yoshino, H., 1994. "Slow dynamics in 3D ± J Heisenberg spin glass; Monte Carlo analysis of auto-correlation functions of individual spins," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 204(1), pages 650-659.
    • Handle: RePEc:eee:phsmap:v:204:y:1994:i:1:p:650-659
    DOI: 10.1016/0378-4371(94)90452-9
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    1. Nemoto, Jiro & Nakanishi, Yasuo & Madono, Seishi, 1993. "Scale Economies and Over-capitalization in Japanese Electric Utilities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 34(2), pages 431-460, May.
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