From measurements to inferences of physical quantities in numerical simulations

TL;DR

This paper introduces a novel inference-based approach for numerical estimation of physical quantities in simulations, enabling more precise, continuous function estimations and insights into phase transitions.

Contribution

It presents a new method for simultaneous, cooperative estimation of physical quantities from raw data, improving precision and allowing continuous function analysis in numerical simulations.

Findings

The method applied to the 3D Heisenberg spin-glass model shows consistent transition temperatures.

The approach reveals a size-crossover effect explaining spin-chirality separation.

Results align with experimental observations of critical exponents.

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.