How do we think of the Kolmogorov Complexity of the Ising Model?
Naively, the K(Ising_Model(T)) \~ T , because we can have a program that only depend on T.
But I heard at criticality Kolmogorov Complexity must be maximum because you have correlation length L(T) \~ |T-T_c|\^-v suggesting statistically you don't need a long program at both ends of T.
You may expand in to Spin Glasses if you know anything about Complexity Theory this way.