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Exploring the Similarities Between Mean-field and Short-range Relaxation Dynamics of Spin Models

Brazilian Journal of Physics volume 52, Article number: 128 (2022) Cite this article

Abstract

In this work, we explore some exciting details of the time-dependent regime in long-range systems under mean-field approximation compared to the critical dynamics of the short-range systems. Firstly, we discuss some mechanisms of the initial anomalous behavior of the magnetization via two and three-dimensional Monte Carlo simulations to later compare with results from mean-field simulations in both: spin 1/2 and spin 1 (Blume–Capel) Ising models. We also investigate the distinction between critical and tricritical points and the corresponding crossover. For a complete analysis, we performed short-time simulations in the mean-field regime to determine the critical temperatures optimizing power laws and the critical exponents of the different points. We independently calculated these exponents, i.e., without using previous exponents estimates from literature/theory. Our investigations corroborate the analytical results here also developed.

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Funding

R. da Silva thanks CNPq for financial support under grant number 311236/2018-9.

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  1. Institute of Physics, UFRGS, Bento Gonçalves, Porto Alegre, 91501-970, Rio Grande do Sul, Brazil

    Roberto da Silva

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  1. Roberto da Silva
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Correspondence to Roberto da Silva.

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da Silva, R. Exploring the Similarities Between Mean-field and Short-range Relaxation Dynamics of Spin Models. Braz J Phys 52, 128 (2022). https://doi.org/10.1007/s13538-022-01135-2

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  • DOI: https://doi.org/10.1007/s13538-022-01135-2

Keywords

  • Tricritical dynamics
  • Crossover effects
  • Time-dependent Monte Carlo simulations
  • Kinetic mean-field equations