The inverse problem beyond two-body interaction: the cubic mean-field Ising model

TL;DR

This paper addresses the inverse problem for a cubic mean-field Ising model, developing methods to reconstruct system parameters from data and testing their robustness across different phase regions.

Contribution

It introduces a solution to the inverse problem for the cubic mean-field Ising model and evaluates its robustness in various thermodynamic phases.

Findings

Successful reconstruction of parameters from configuration data

Robustness of the inversion method in multiple phase regions

Identification of conditions for unique solutions

Abstract

In this paper we solve the inverse problem for the cubic mean-field Ising model. Starting from configuration data generated according to the distribution of the model we reconstruct the free parameters of the system. We test the robustness of this inversion procedure both in the region of uniqueness of the solutions and in the region where multiple thermodynamics phases are present.