A new approach to dynamic finite-size scaling

TL;DR

This paper introduces a novel method using Taylor series expansion of dynamic scaling relations to analyze finite-size effects in Ising models, enabling separate estimation of dynamic exponents.

Contribution

The work presents a new approach to study dynamic finite-size scaling in Ising models, allowing separate calculation of dynamic exponents $z$ and $x_0$.

Findings

Good agreement with literature values for critical exponents

Method effectively captures dynamic scaling behavior

Applicable to different lattice sizes

Abstract

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behaviour of 2- and 3-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent $x_0$ to observe the dynamic finite-size scaling behaviour of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For 3-dimensional Ising Model we have also presented that this method opens the possibility of calculating $z$ and $x_0$ separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.