Replica Trick

In the statistical physics of spin glasses and other systems with quenched disorder, the replica trick is a mathematical technique for computing the disorder average of the logarithm of a system partition function. It exploits the identity that the logarithm of a quantity Z equals the limit, as an exponent n approaches zero, of Z raised to the n minus one, divided by n. This identity lets the difficult problem of averaging a logarithm be replaced by the more tractable problem of averaging Z raised to an integer power n, treating n copies, or replicas, of the same disordered system together before eventually taking the limit as n goes to zero. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/