Nonequilibrium dynamic-correlation-length scaling method

TL;DR

This paper introduces a novel nonequilibrium dynamic-correlation-length scaling method that improves the analysis of phase transitions in spin models by addressing limitations of traditional finite-size and finite-time scaling techniques.

Contribution

The paper proposes a new scaling method based on dynamic correlation length for nonequilibrium relaxation data, providing more accurate estimates of critical parameters.

Findings

Successfully applied to 3D Ising models and spin glasses

Accurately determined transition temperature and critical exponents

Highlighted issues with the Ornstein-Zernike formula in nonequilibrium

Abstract

The finite-size scaling method in the equilibrium Monte Carlo(MC) simulations and the finite-time scaling method in the nonequilibrium-relaxation simulations are compromised. MC time data of various physical quantities are scaled by the MC time data of the dynamic correlation length, which corresponds to changing the system size in the finite-size scaling method. This scaling method is tested in the three-dimensional ferromagnetic Ising spin model and in the three dimensional $\pm J$ Ising spin-glass model. The transition temperature and the critical exponents, $\eta$ and $\nu$, are obtained by the nonequilibrium relaxation data of the susceptibility and the dynamic correlation length apart from the dynamic exponent. We also comment on the definition of the dynamic correlation length in the nonequilibrium relaxation process. The Ornstein-Zernike formula is not always appropriate.