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:
or:
where
is most commonly the partition function, or a similar thermodynamic function.
It is typically used to simplify the calculation of , the expected value of , reducing the problem to calculating the disorder average where is assumed to be an integer. This is physically equivalent to averaging over copies or replicas of the system, hence the name.
The crux of the replica trick is that while the disorder averaging is done assuming to be an integer, to recover the disorder-averaged logarithm one must send continuously to zero. This apparent contradiction at the heart of the replica trick has never been formally resolved, however in all cases where the replica method can be compared with other exact solutions, the methods lead to the same results. (A natural sufficient rigorous proof that the replica trick works would be to check that the assumptions of Carlson's theorem hold, especially that the ratio is of exponential type less than π.)
It is occasionally necessary to require the additional property of replica symmetry breaking (RSB) in order to obtain physical results, which is associated with the breakdown of ergodicity.
physics of spin glasses and other systems with quenched disorder, the replicatrick is a mathematical technique based on the application of the formula:...
in terms of systematic applications of the replica method to disordered systems, even though the replica method itself was originally discovered in 1971...
techniques used to analyzed systems with quenched disorder include the replicatrick, based on analytic continuation, and the cavity method, where a system's...
also solvable using the replicatrick but has the advantage of being more intuitive and less mathematically subtle than replica-based methods. The cavity...
supersymmetry method provides a mathematical rigorous alternative to the replicatrick, but only in non-interacting systems, which attempts to address the...
Orientational glass Phase transition Quenched disorder Random energy model Replicatrick Solid-state physics Spin ice T c {\displaystyle T_{\text{c}}} is identical...
using the replicatrick. The path integral that computes the entropy receives contributions from novel Euclidean configurations called "replica wormholes"...
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