From measurements to inferences of physical quantities in numerical simulations

Abstract

We propose a change of style for numerical estimations of physical quantities from measurements to inferences. We estimate the most probable quantities for all the parameter region simultaneously by using the raw data cooperatively. Estimations with higher precisions are made possible. We can obtain a physical quantity as a continuous function, which is differentiated to obtain another quantity. We applied the method to the Heisenberg spin-glass model in three dimensions. A dynamic correlation-length scaling analysis suggests that the spin-glass and the chiral-glass transitions occur at the same temperature with a common exponent $\nu$. The value is consistent with the experimental results. We found that a size-crossover effect explains a spin-chirality separation problem.

5 pages, 5 figures, revised

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• Finite spin-glass transition of the $\pm J$ XY model in three dimensions
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Cited by in corpus (7)

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• Sine-square deformation applied to classical Ising models
• Machine learning as an improved estimator for magnetization curve and spin gap
• A strategy for solving difficulties in spin-glass simulations
• Improvement of analysis for relaxation of fluctuations by the use of Gaussian process regression and extrapolation method
• Dynamical scaling method improved by a deep learning approach
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices