Usually in statistical physics, high temperature phases are disordered and featureless while low temperature phases are 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!), along with high-temperature superfluidity. Applications and implications of entropic order at high temperature will be discussed, including in high energy theory and quantum information.
Event
Lewis Lab, 316
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