Kernel method for corrections to scaling

Abstract

Scaling analysis, in which one infers scaling exponents and a scaling function in a scaling law from given data, is a powerful tool for determining universal properties of critical phenomena in many fields of science. However, there are corrections to scaling in many cases, and then the inference problem becomes ill-posed by an uncontrollable irrelevant scaling variable. We propose a new kernel method based on Gaussian process regression to fix this problem generally. We test the performance of the new kernel method for some example cases. In all cases, when the precision of the example data increases, inference results of the new kernel method correctly converge. Because there is no limitation in the new kernel method for the scaling function even with corrections to scaling, unlike in the conventional method, the new kernel method can be widely applied to real data in critical phenomena.

8 pages, 5 figures, the reference code of this new method is prepared at http://kenjiharada.github.io/BSA/

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• "Deconfined" quantum critical points
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• A Scaling Relation for Dangerously Irrelevant Symmetry-Breaking Fields
• Path-integral Monte Carlo method for the local Z_2 Berry phase
• Thermal Phase Transition of Generalized Heisenberg Models for SU(N) Spins on Square and Honeycomb Lattices
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