Replica trick
In the statistical physics of spin glasses and other systems with quenched disorder, the replica trick is a mathematical technique based on the application of the formula: ln Z = lim n → 0 Z n − 1 n {\displaystyle \ln Z=\lim _{n\to 0}{Z^{n}-1 \over n}} or: ln Z = lim n → 0 ∂ Z n ∂ n {\displaystyle \ln Z=\lim _{n\to 0}{\frac {\partial Z^{n}}{\partial n}}} where Z {\displaystyle Z} is most commonly the partition function, or a similar thermodynamic function. It is typically used to simplify the calculation of ln Z ¯ {\displaystyle {\overline {\ln Z}}} , the expected value of ln Z {\displaystyle \ln Z} , reducing the problem to calculating the disorder average Z n ¯ {\displaystyle {\overline {Z^{n}}}} where n {\displaystyle n} is assumed to be an integer.