  The total many-body correlations present in finite temperature classical spin
systems are studied using the concept of mutual information. As opposed to
zero-temperature quantum phase transitions, the total correlations are not
maximal at the phase transition, but reach a maximum in the high temperature
paramagnetic phase. The Shannon and Renyi mutual information in both Ising and
Potts models in 2 dimensions are calculated numerically by combining matrix
product states algorithms and Monte Carlo sampling techniques.
