We obtain the mutual information of Ising systems, which shows singular behavior near the critical point. We connect the mutual information with the magnetization and the correlation function. The mutual information is a suitable measure for the critical behavior of Ising systems.
I. I N T R O D U C T I O NLet AB be a joint system consisting of individual systems A and B. If A has states { et } and B has states { 13 }, AB has joint states { ctl3 }. The probability distributions of these systems are given by = = where p~ and p~ denote the probabilities that A is in ct and B is in 13, respectively, and p~ denotes the joint probability that AB is in ct13. The mutual information (Shannon, 1948) between A and B is defined bywhere St (SB) is the individual entropy of A (B) and SAS is the joint entropy of AB as follows: Sa = -2 P~ log p~, Sn = -~ p~ log p~ (3) San = -~] p~ log pA~ (4)
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