Off-equilibrium relaxational dynamics with improved Ising Hamiltonian

TL;DR

This study investigates the off-equilibrium relaxational dynamics at criticality in a 3D Ising universality class model using improved Hamiltonian Monte Carlo simulations, providing a precise estimate of the dynamical critical exponent.

Contribution

It presents the first Monte Carlo estimate of the dynamical critical exponent for the 3D Ising universality class using an improved Hamiltonian to minimize scaling corrections.

Findings

Estimated dynamical critical exponent z=2.020(8)

Results are consistent with Field Theory predictions

Demonstrates effectiveness of improved Hamiltonian in simulations

Abstract

We study the off-equilibrium relaxational dynamics at criticality in the three-dimensional Blume-Capel model whose static critical behaviour belongs to the 3d-Ising universality class. Using "improved" Hamiltonian (the leading corrections to scaling have vanishing amplitude) we perform Monte Carlo simulations of the relaxational dynamics after a quench from $T=\infty$ to $T_c$. Analysing the off-equilibrium dynamics at $T_c$ we obtain an estimate of the dynamical critical exponent $z=2.020(8)$ that is perfectly consistent with the Field Theory predictions.