# Computation of the dynamic critical exponent of the three-dimensional Heisenberg model

## TL;DR

This paper accurately computes the dynamic critical exponent of the three-dimensional Heisenberg model using advanced equilibrium and out-of-equilibrium techniques, providing results consistent with previous studies and experiments.

## Contribution

It presents the first high-precision computation of the dynamic critical exponent for large lattices in the 3D Heisenberg model using both equilibrium and out-of-equilibrium methods.

## Key findings

- Dynamic critical exponent z ≈ 2.03–2.04
- Consistent static critical exponents η and ν
- Agreement with previous small-lattice and theoretical estimates

## Abstract

Working in and out of equilibrium and using state-of-the-art techniques we have computed the dynamic critical exponent of the three dimensional Heisenberg model. By computing the integrated autocorrelation time at equilibrium, for lattice sizes $L\le 64$, we have obtained $z=2.033(5)$. In the out of equilibrium regime we have run very large lattices ($L\le 250$) obtaining $z=2.04(2)$ from the growth of the correlation length. We compare our values with that previously computed at equilibrium with relatively small lattices ($L\le 24$), with that provided by means a three-loops calculation using perturbation theory and with experiments. Finally we have checked previous estimates of the static critical exponents, $\eta$ and $\nu$, in the out of equilibrium regime.