Thermal induced order, from Rochelle salt to dirty superconductors

Common wisdom dictates that physical systems become less ordered when heated to higher temperature. But is that inevitable? In this talk I will discuss a set of simple models that displays the opposite phenomenon and order upon increasing the temperature. I will argue that these models describe a wide array of physical systems, and that their phenomenology is robust to the underlying details. Some analytically tractable limits will be discussed, but most of the talk will be based on numerical results obtained with belief propagation (of tensor networks). Finally, I will discuss some simple variational RG that captures the basic phenomenon.