Work

Learning and Testing Inverse Statistical Problems For Interacting Systems Undergoing Phase Transition

Year: 2025

Type: preprint

Abstract: Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of techniques to address this challenge. In this work, we illustrate three of the main methods: the Maximum Likelihood, Maximum Pseudo-Likelihood, and Mean-Field approaches. We begin with a thorough theoretical introduction to these methods, followed by their application to inference in several well-known statistical physics systems undergoing phase transitions. Namely, we consider the ordered and disordered Ising models, the vector Potts model, and the Blume-Capel model on both regular lattices and random graphs. This discussion is accompanied by a GitHub repository that allows users to both reproduce the results and experiment with new systems.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2507.02574

Authors: Bae, Stefano, Bocchi, Dario, Del Bono, Luca Maria, Leuzzi, Luca

Institutions: Institute of Nanotechnology, National Research Council, Sapienza University of Rome

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Digital Research Infrastructure for the Arts and Humanities, National Nanotechnology Center

OpenAlex ID: W6891963140

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