Replica trick

Summary

The replica trick computes the average of the logarithm of a random partition function from the averages of its integer powers. It rests on the identity $\log Z = \lim_{n \to 0} (Z^n - 1)/n$. For an integer $n$, the power $Z^n$ is the partition function of $n$ independent copies, or replicas, of the system with the same disorder. It is the main heuristic tool behind the theory of spin glasses. Some of its predictions, such as the Parisi formula, were later proved by other methods.