Strategy for solving difficulties in spin-glass simulations

Tota Nakamura
Phys. Rev. E 99, 023301 – Published 4 February 2019

Abstract

A spin-glass transition has been investigated for a long time but we have not reached a conclusion yet due to difficulties in the simulation studies. They are slow dynamics, strong finite-size effects, and sample-to-sample dependencies. We found that a size of the spin-glass order reaches a lattice boundary within a very short Monte Carlo step. A competition between the spin-glass order and a boundary condition causes these difficulties. Once the boundary effect was removed, physical quantities exhibited quite normal behaviors. They became self-averaging in a limit of large replica numbers. These findings suggest that the nonequilibrium relaxation method is a good choice for solving the difficulties if a lattice size and a replica number are set sufficiently large. A dynamic scaling analysis on nonequilibrium relaxation functions gave a result that the spin-glass transition and the chiral-glass transition occurs at the same temperature in the Heisenberg model in three dimensions. The estimated critical exponent ν agrees with the experimental result.

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  • Received 22 September 2018
  • Revised 22 November 2018

DOI:https://doi.org/10.1103/PhysRevE.99.023301

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Tota Nakamura

  • Faculty of Engineering, Shibaura Institute of Technology, 307 Fukasaku, Minuma, Saitama 337-8570, Japan

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Issue

Vol. 99, Iss. 2 — February 2019

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