Work

The variational principle for a marked Gibbs point process with infinite-range multibody interactions

Year: 2025

Type: article

Abstract: We prove the Gibbs variational principle for the Asakura–Oosawa model in which particles of random size obey a hardcore constraint of non-overlap and are additionally subject to a temperature-dependent area interaction. The particle size is unbounded, leading to infinite-range interactions, and the potential cannot be written as a k-body interaction for fixed k. As a byproduct, we also prove the existence of infinite-volume Gibbs point processes satisfying the DLR equations. The essential control over the influence of boundary conditions can be established using the geometry of the model and the hard-core constraint.

Source: Electronic Journal of Probability

DOI: 10.1214/25-ejp1441

Authors: Benedikt Jahnel, Jonas Köppl, Yannic Steenbeck, Alexander Zass

Institutions: Weierstrass Institute for Applied Analysis and Stochastics, Technische Universität Braunschweig

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Deutsche Forschungsgemeinschaft, Leibniz-Gemeinschaft