Non-equilibrium relaxation and interface energy of the Ising model

TL;DR

This paper investigates non-equilibrium relaxation dynamics and interface energy properties of the Ising model, providing new estimates for critical exponents and demonstrating a Monte Carlo renormalization approach.

Contribution

It introduces precise estimates of critical exponents for the 2D and 3D Ising models and applies a dynamic Monte Carlo renormalization group method to study their equilibrium properties.

Findings

Dynamical critical exponent z = 2.165 ± 0.010 for 2D Ising model.

Relaxation in the ordered phase follows exp(-√t/τ) behavior.

Critical exponent ν = 0.6250 ± 0.025 and surface tension amplitude σ₀ = 1.42 ± 0.04 for 3D Ising model.

Abstract

{}From the non-equilibrium critical relaxation study of the two-dimensional Ising model, the dynamical critical exponent $z$ is estimated to be $2.165 \pm 0.010$ for this model. The relaxation in the ordered phase of this model is consistent with $\exp (-\sqrt{t/\tau })$ behavior. The interface energy of the three-dimensional Ising model is studied and the critical exponent of the correlation length $\nu$ and the critical amplitude of the surface tension $\sigma_0$ are estimated to be $0.6250\pm 0.025$ and $1.42\pm 0.04$, respectively. A dynamic Monte Carlo renormalization group method is applied to the equilibrium properties of the three-dimensional Ising model successfully.