Question

Why Potts model has a first order phase transition when the state number is large enough?

Answer 1

I have known the fact that Potts model has first-order phase transition in 2D when the number of states q>4q>4. And similar behavior happens in 3D and 4D etc. I also know that there is some proof of the fact, both from physicist like Rodney Baxter or mathematican like Hugo Duminil-Copin. However it is not easy for me to draw some understand from these highly-technical arguments.

Answer 2

We show the existence of a first-order phase transition in the v-dimensional Potts model for v ^ 2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature.