Probability Distribution Function of the Order Parameter: Mixing Fields and Universality

Abstract

We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin magnetic systems on a lattice, such as Ising, general spin-$S$ Blume-Capel and Baxter-Wu, $Q$-state Potts, among other models, will be considered as examples. The importance and the necessity of the role of mixing fields in asymmetric magnetic models will be discussed in more detail, as well as the corresponding distributions of the extensive conjugate variables.

14 pages, 13 figures, accepted for publication (Computer Physics Communications)

References in corpus (4)

• More is the Same; Phase Transitions and Mean Field Theories
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Square Lattice Gases with Two- and Three-body Interactions Revisited
• Probability distribution of the order parameter in the directed percolation universality class

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• The Blume-Capel model for spins S=1 and 3/2 in dimensions d=2 and 3
• First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited
• Critical Binder cumulant and universality: Fortuin-Kasteleyn clusters and order-parameter fluctuations
• Phase Diagram of the $J_1$ - $J_2$ Frustrated Anisotropic Antiferromagnet with Spin $S=1$ on the Quadratic Lattice
• Emergent Coulombic criticality and Kibble-Zurek scaling in a topological magnet
• Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet
• Exploring the nature of chiral phase transition in two-flavor QCD using extra heavy quarks
• High-resolution Monte Carlo study of the order-parameter distribution of the three-dimensional Ising model
• Universal energy and magnetisation distributions in the Blume-Capel and Baxter-Wu models
• Liquid-gas analog multicriticality in a frustrated Ising bilayer
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process