The Nishimori line and Bayesian Statistics

TL;DR

This paper reinterprets the Nishimori line in disordered systems through Bayesian statistics, linking it to error-correcting codes and providing new insights into its theoretical foundations and applications.

Contribution

It offers a novel Bayesian perspective on the Nishimori line, connecting statistical physics with information theory and error-correcting codes.

Findings

Reconstruction of Nishimori line theory via Bayesian statistics

Identification of Nishimori line counterparts in non-gauge models

Discussion on finite temperature decoding and gauge invariance

Abstract

``Nishimori line'' is a line or hypersurface in the parameter space of systems with quenched disorder, where simple expressions of the averages of physical quantities over the quenched random variables are obtained. It has been playing an important role in the theoretical studies of the random frustrated systems since its discovery around 1980. In this paper, a novel interpretation of the Nishimori line from the viewpoint of statistical information processing is presented. Our main aim is the reconstruction of the whole theory of the Nishimori line from the viewpoint of Bayesian statistics, or, almost equivalently, from the viewpoint of the theory of error-correcting codes. As a byproduct of our interpretation, counterparts of the Nishimori line in models without gauge invariance are given. We also discussed the issues on the ``finite temperature decoding'' of error-correcting codes in connection with our theme and clarify the role of gauge invariance in this topic.