Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics

TL;DR

This study investigates the short-time critical dynamics of the two-dimensional Blume-Capel model at tricritical and critical points, estimating dynamic and static exponents through scaling analysis.

Contribution

It provides new estimates of dynamic exponents at the tricritical point of the 2D Blume-Capel model using short-time dynamics methods.

Findings

Dynamic exponent z=2.215(2) at tricritical point

Initial slip exponent θ= -0.53(2) at tricritical point

Scaling relations effectively describe early-stage magnetization behavior

Abstract

In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are $z= 2.215(2)$ and $\theta= -0.53(2)$.