Replica symmetry breaking related to a general ultrametric space III: the case of general measure

TL;DR

This paper introduces a family of replica matrices based on general ultrametric spaces with measures, extending Parisi matrices, and computes related functionals to find a replica symmetry breaking solution.

Contribution

It generalizes known replica matrices to broader ultrametric spaces with measures and derives a replica symmetry breaking solution.

Findings

Introduced a new family of replica matrices for general ultrametric spaces.

Computed functionals related to the replica approach.

Derived a replica symmetry breaking solution.

Abstract

Family of replica matrices, related to general ultrametric spaces with general measures, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed. Replica symmetry breaking solution is found.