Surprising statistical physics with an infinity of microstates

Abstract: In this colloquium I will describe two simple classical models, each of which has a very surprising phase diagram at finite temperature.   Firstly, I will describe a simple model on a two-dimensional lattice, whose ground state is a gas and which heats into a solid at finite temperature, remaining a solid forever upon further heating.   Secondly, I will describe a simple one-dimensional model which spontaneously breaks a discrete symmetry at any temperature.  Both of these observations are clear counterexamples to conventional wisdom.  I will explain how the presence of an infinite number of available microstates enables us to break this conventional wisdom, while each problem remains mathematically well-defined (the thermal ensemble exists, etc.).

These cartoon models are fun, but they were each motivated by more serious questions in physics, which I will also describe.   The first model was developed to answer a simple question from quantum field theory:  why do some theories spontaneously break a symmetry at any positive temperature?   The second model was designed to demonstrate  an error-correcting code with a simple decoder that is very robust to noise.   Interestingly, generalizing the classical construction to a quantum code faces a surprising obstruction from mathematics.

Biography:  Andrew Lucas is an associate professor of physics at the University of Colorado Boulder.  His main interests are in theoretical and mathematical physics, particularly at the interface between traditionally distinct communities.  Some of his awards include a Sloan Fellowship (2020), NSF CAREER (2022), AFOSR YIP (2024), and the George E. Valley Jr. Prize from APS (2022).