Replica symmetry breaking related to a general ultrametric space I: replica matrices and functionals

TL;DR

This paper introduces a family of replica matrices based on ultrametric spaces, generalizing Parisi matrices, and computes related functionals within the replica approach.

Contribution

It presents a new class of replica matrices linked to ultrametric spaces and extends the computation of functionals beyond known models.

Findings

Introduces a family of ultrametric-based replica matrices.

Generalizes the structure of Parisi matrices.

Computes specific functionals of the replica approach.

Abstract

Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.