Francesco Guerra - The replica trick on interpolating replicas

We review the historical development of the replica trick, and point out the great power of the method. The traditional interpretation is based on analytic continuation with respect to the number of replicas. From this point of view, replica symmetry and replica symmetry breaking are connected to a different choice of analytic continuations starting from an integer number of replicas. A different possible interpretation is based on direct interpolation on the number of replicas. Then replica symmetry breaking corresponds to a phase transition. Derrida Random Energy Model gives the simplest example for the interpolating replica trick. We give also some recent results on the rigorous proof that the Almeida-Thouless line is the line of replica symmetry breaking for the Sherrington-Kirkpatrick model in random external field.

40 years of Replica Symmetry Breaking
10-13 September 2019, Rome

replicas