Event-chain algorithm for the Heisenberg model: Evidence for $z \simeq 1$ dynamic scaling

TL;DR

This paper demonstrates that the event-chain Monte Carlo algorithm significantly reduces the dynamical critical exponent to approximately 1 in the 3D Heisenberg model, indicating faster convergence near criticality.

Contribution

It introduces an event-chain Monte Carlo algorithm for the Heisenberg model that achieves a lower dynamical critical exponent than traditional methods.

Findings

Autocorrelation functions show z ≈ 1 at criticality.

The algorithm is rejection-free and satisfies global balance.

First evidence of reduced critical slowing down with this method.

Abstract

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent $z \approx 1$ at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. This seems to be the first report that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of $z\simeq 2$.