Affinities and disagreements between Mean-field and short-range critical\n dynamics

2021/08/02 by Roberto da Silva, da Silva, Roberto
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2108.00636

openalex publication_date 2021/08/02 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this work, we explore some interesting details of the time-dependent\nregime of the long-range systems under mean-field approximation in comparison\nwith the critical dynamics of the short-range systems. First, we discuss some\nmechanisms of the initial anomalous behavior of the magnetization via\ntwo-dimensional Monte Carlo simulations to later compare with results from\nMean-field simulations in both: spin 1/2 (Ising) and spin 1 (Blume Capel model)\nIsing models. The distinction between critical and tricritical points is also\ninvestigated. For a complete analysis, we performed short-time simulations in\nthe mean-field regime to determine the critical temperatures optimizing power\nlaws and the critical exponents of the different points, which were\nindependently calculated, i.e. without using previous critical exponents\nestimates from literature/theory. Our investigations corroborate analytical\nresults here also developed.\n

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