Inverse problem for the mean-field monomer-dimer model with attractive interaction

TL;DR

This paper investigates an inverse problem approach for a mean-field monomer-dimer model with attractive interactions, using analytical and maximum-likelihood methods to identify parameters and address ambiguities near phase coexistence.

Contribution

It introduces an analytical and maximum-likelihood framework for solving the inverse problem in a monomer-dimer model with phase transitions, including handling ambiguities near critical points.

Findings

High precision in parameter identification across phase space

Effective handling of ambiguities near the coexistence line

Validation of the inverse method with clustering techniques

Abstract

The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion.