Bayesian inference in the scaling analysis of critical phenomena

2011/02/28 by Kenji Harada · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Critical exponent #Critical phenomena #Critical point (mathematics) #Geometry #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Quantum mechanics #Renormalization group #Scaling #Smoothness #Square (algebra) #Square lattice #Statistical physics #Theoretical and Computational Physics #Topological and Geometric Data Analysis #Universality (dynamical systems) #Widom scaling #cond-mat.stat-mech #cond-mat.str-el #physics.comp-ph #physics.data-an

paper · pdf · doi:10.1103/physreve.84.056704

published as Phys. Rev. E 84, 056704 (2011) · 7 pages, 8 figures, and 1 table

arxiv created 2011/11/18 · openalex publication_date 2011/11/18 · arxiv updated 2011/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

To determine the universality class of critical phenomena, we propose a method of statistical inference in the scaling analysis of critical phenomena. The method is based on Bayesian statistics, most specifically, the Gaussian process regression. It assumes only the smoothness of a scaling function, and it does not need a form. We demonstrate this method for the finite-size scaling analysis of the Ising models on square and triangular lattices. Near the critical point, the method is comparable in accuracy to the least-square method. In addition, it works well for data to which we cannot apply the least-square method with a polynomial of low degree. By comparing the data on triangular lattices with the scaling function inferred from the data on square lattices, we confirm the universality of the finite-size scaling function of the two-dimensional Ising model.

Citations

• Lectures on Phase Transitions and the Renormalization Group
• Cluster analysis and finite-size scaling for Ising spin systems
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• The Spontaneous Magnetization of a Two-Dimensional Ising Model

Cited by

• Critical behavior of the two-dimensional icosahedron model
• Finite-m scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

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• Critical point determination from probability distribution functions in the three dimensional Ising model