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Title: Bayesian inference in the scaling analysis of critical phenomena
Authors: Harada, Kenji  kyouindb  KAKEN_id
Author's alias: 原田, 健自
Issue Date: 18-Nov-2011
Publisher: American Physical Society
Journal title: Physical Review E
Volume: 84
Issue: 5
Thesis number: 056704
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.
Rights: ©2011 American Physical Society
DOI(Published Version): 10.1103/PhysRevE.84.056704
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