Ian Jauslin

The liquid-vapor phase transition in a system with a finite but coarse-grained attraction

AMS 2026 Fall Eastern Sectional Meeting, Partial Differential Equations and Optimal Transportation, George Washington University, Washington DC, USA

October 4, 2026

The standard approach to studying the liquid-vapor phase transition uses the Maxwell double-tangent construction. Whereas this construction is easily justified physically, deriving it mathematically has proved to be more difficult. In 1966, Lebowitz and Penrose proved the Maxwell construction in a mean field model, where the particles interact via a hard-core repulsion, and an infinite range, infinitely weak attraction. Generalizing their result to finite pair attractions remains an open problem.

In this talk, I will discuss a proof of the existence of a liquid-vapor phase transition in a system with an attraction that is finite, but is also coarse-grained. More precisely, we split up space into mesoscopic boxes, and define an attraction that ignores the location of the particles within each box. Defined in this way, our model is reflection positive, which allows us to prove the existence of a liquid-vapor phase transition.

This is joint work with Qidong He, Joel L. Lebowitz, and Ron Peled.

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