# The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model

## TL;DR

This paper uses Monte Carlo simulations of the improved Blume-Capel model to accurately estimate the dynamic critical exponent $z$ in the three-dimensional Ising universality class, confirming recent theoretical predictions.

## Contribution

It provides a precise numerical estimate of the dynamic critical exponent $z$ using finite size scaling and quenched configurations, aligning with field theoretic results.

## Key findings

- Estimated $z=2.0245(15)$ for the dynamic critical exponent.
- Consistent results from quenched magnetized configurations.
- Agreement with recent field theoretic estimates.

## Abstract

We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain $z=2.0245(15)$ for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our estimate of $z$ is fully consistent with recent field theoretic results.