I will talk about the Ising model -- the drosophila of the rigorous statistical physics. It turns out that some of the new phenomena which appear in modern mathematical physics can still be observed in the Ising model as well. 
One example which I will focus on is the size of typical fluctuations of the extended systems. If the size of the system is N, then the usual (Gaussian) fluctuations are of the order of N^{1/2}. Bit in the random matrix theory one sees the fluctuations of the order N^{1/3}. I will explain that one can see them already in the Ising model -- one just needs to know where to look.