Understand
In this paper we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas.
- The basic tool of this technique is a distributional zeta-function, a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which can not be written as a series of the integer moments, can be made as small as desired.
- This result supports the use of integer moments of the partition function, computed via replicas, for expressing the average free energy of the system.
- One advantage of the proposed formalism is that it does not require the understanding of the properties of the permutation group when the number of replicas goes to zero.