First-order phase transition for Gibbs point processes with saturated interactions

TL;DR

This paper establishes the existence of first-order phase transitions in continuum Gibbs point processes with saturated interactions, using an adapted Pirogov-Sinai theory to demonstrate multiple Gibbs measures.

Contribution

It introduces a general method for proving phase transitions in Gibbs point processes with saturated interactions, extending previous models and applying to new classes of interactions.

Findings

Existence of two distinct infinite-volume Gibbs measures with different densities.

Development of a general method based on Pirogov-Sinai-Zahradnik theory.

Application to new classes of diluted pairwise interactions.

Abstract

We study first-order phase transitions in continuum Gibbs point processes with saturated interactions. These interactions form a broad class of Hamiltonians in which the local energy in regions of high particle density depends only on the number of points. Building on ideas of Pirogov-Sinai-Zahradnik theory and its adaptations to the continuum, we develop a general method for establishing the existence of two distinct infinite-volume Gibbs measures with different intensities in this setting, demonstrating a first-order phase transition. Our approach extends previous results obtained for the Quermass model and applies in particular to a new class of diluted pairwise interactions introduced in this work.