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IN-PERSON MATHEMATICAL PHYSICS SEMINAR
RUTGERS UNIVERSITY
HILL 705
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Ian Jauslin – Rutgers University
Date/Time/Location
Thursday, October 10th, 2:00 pm; Hill Center 705
A liquid-vapor phase transition in a simple model
At 100 degrees Celsius, liquid water boils and transitions to a gas state. This transition is a first-order phase transition, between a phase where particles interact weakly, to one in which they interact strongly. Because strongly interacting particle systems are difficult to study, this phase transition is not so easy to understand. In the XIXth century, Maxwell introduced a procedure that reproduces the thermodynamic properties that were measured experimentally. However, the theoretical justification of Maxwell's construction from first principles is notoriously difficult. In a breakthrough paper that appeared in 1966, J.L. Lebowitz and O. Penrose derived the Maxwell construction starting from a microscopic model, in which particles interact via a so-called Kac potential, which is infinitely weak and infinitely long-range (in this sense, their result is a mean-field one). Since then, there has been much work in attempting to extend this result to systems of particles with weak (but finite) interactions over large (but finite) range. Lebowitz, Mazel, and Presutti managed to do just that in 1998-99 for a model of particles with a Kac-type attraction, but also a long range four-body repulsion. It is still an open problem to extend the Lebowitz-Penrose result to models with a pair interaction, which is more natural than the four-body potential of Lebowitz, Mazel, and Presutti. In this talk, I will present work in progress in which we define a simplified interacting particle model, with a pair interaction. This model is a coarse-grained version of one in which particles interact via an attractive Kac potential, as well as a (repulsive) hard-core interaction. We prove that this model is reflection-positive, which allows us to easily prove the existence of a phase transition that has all of the hallmarks of the liquid-vapor transition. This model is thus one in which the liquid-vapor phase transition can be understood with minimal effort, while being somewhat realistic, by virtue of having only pairwise interactions between particles.
This is joint work with Qidong He, Joel L. Lebowitz, Ron Peled