A strategy for solving difficulties in spin-glass simulations

TL;DR

This paper introduces a new dynamic scaling analysis method to overcome simulation difficulties in studying spin-glass transitions, revealing that boundary effects are the main obstacle and confirming simultaneous spin- and chiral-glass transitions with consistent critical exponents.

Contribution

It proposes a novel approach to eliminate boundary effects in spin-glass simulations, enabling clearer observation of phase transitions and critical behavior.

Findings

Boundary effects are the main cause of simulation difficulties.

Spin-glass and chiral-glass transitions occur at the same temperature.

Critical exponent ν matches experimental results.

Abstract

A spin-glass transition has been investigated for a long time but we have not yet reached a conclusion due to difficulties in the simulations. They are slow dynamics, strong finite-size effects, and sample-to-sample dependences. We clarified that these difficulties are mainly caused by a competition between the spin-glass order and the boundary conditions. We also found that the spin-glass order grows fast and reaches the lattice boundary within a very short Monte Carlo step. A key to solve the difficulties is to eliminate the boundary effect first. It was made possible by a dynamic scaling analysis on nonequilibrium relaxation functions in a large-size and short-time regime. The observed quantity was also found to be self-averaging in a limit of large replica number. The spin-glass transition and the chiral-glass transition was clarified to occur at the same temperature in the Heisenberg spin-glass model in three dimensions. The estimated critical exponent $\nu$ agrees with the experimental result.