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Critical and tricritical singularities from small-scale Monte Carlo simulations: the Blume–Capel model in two dimensions

Authors
  • Moueddene, Leïla
  • G Fytas, Nikolaos
  • Holovatch, Yurij
  • Kenna, Ralph
  • Berche, Bertrand
Type
Published Article
Journal
Journal of Statistical Mechanics: Theory and Experiment
Publisher
IOP Publishing
Publication Date
Feb 12, 2024
Volume
2024
Issue
2
Identifiers
DOI: 10.1088/1742-5468/ad1d60
Source
ioppublishing
Keywords
Disciplines
  • Paper section: Classical statistical mechanics, equilibrium and non-equilibrium
License
Unknown

Abstract

We show that accurate insights into the critical properties of the Blume–Capel model at two dimensions can be deduced from Monte Carlo simulations, even for small system sizes, when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricritical point, then a line of first-order transitions. We concentrate on critical and tricritical properties and compare the accuracy achieved via standard finite-size scaling of thermodynamic quantities with that from the zeros analysis. This latter analysis showcases spectacular precision, even for systems as small as 64 spins. We also show that the zeros are very sensitive to subtle crossover effects.

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