Ordered phases of matter at arbitrarily high temperature

by Andrew Lucas (University of Colorado, Boulder)

Monday 22 Sept 2025, 14:00 → 15:00 Europe/Rome

Aula Magna

Usually in statistical physics, high temperature phases are disordered and featureless while low temperature phases may be ordered.  For example, solid ice becomes liquid water upon heating; the solid is an ordered phase that spontaneously breaks translational and rotational symmetries, while the liquid is a disordered phase which restores these symmetries in a typical state.  In fact, mathematicians have proved that many classes of common models in statistical physics, such as interacting spins in lattice models, always enter a disordered phase at  sufficiently high temperature.  On the other hand,  counterexamples to the intuition that heating destroys order have also been known for a long time:  for example, helium-3 under very high pressure can go from a liquid to a solid after heating it at very low temperature.   As I will explain, any such transition from disorder to order upon heating is necessarily characterized by “entropic order”, where ordering one degree of freedom enables many more fluctuations in another, causing entropy (not energy) to stabilize an ordered phase.   I will then show how to build an entropically-ordered phase of matter at arbitrarily high temperature, with a few simple and illustrative examples of lattice gases that heat into solids (and remain solids forever upon further heating!).  I will also explain how entropic order underlies the recent demonstration that 2+1d conformal field theories that spontaneously break Z2 symmetry at finite temperature, exist, and how to use these field theoretic ideas to build a toy model of high-temperature superconductivity, stabilized by entropic order.