Inference for interacting linear waves in ordered and random media

TL;DR

This paper develops a statistical inference method for pairwise interacting systems with continuous angular variables, applicable to both ordered and disordered media, tested via simulations.

Contribution

It introduces a new inference approach for systems with complex and real couplings, extending to complex media and various topologies.

Findings

Successfully infers coupling matrices from correlation data.

Works for both deterministic and disordered couplings.

Validated through Monte Carlo simulations.

Abstract

A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We investigate systems with both deterministic and quenched disordered couplings on two extreme topologies: complete and sparse graphs. To match further applications in optics also complex couplings and external fields are considered and general inference formulas are derived for real and imaginary parts of Hermitian coupling matrices from real and imaginary parts of complex correlation functions. The whole procedure is, eventually, tested on numerically generated correlation functions and local magnetizations by means of Monte Carlo simulations.