Replica Condensation and Tree Decay

TL;DR

The paper introduces a novel method using local cyclic replica symmetry to demonstrate exponential decay in correlations, applicable to various physical systems, by isolating replica condensation effects.

Contribution

It presents a new intuitive approach leveraging replica symmetry to prove exponential decay in correlations, with potential applications beyond the illustrated Ising model.

Findings

Demonstrates exponential tree decay in a low-temperature Ising system

Introduces a method based on replica symmetry and condensation

Provides an entropy bound for random lattice surfaces

Abstract

We give an intuitive method--using local, cyclic replica symmetry--to isolate exponential tree decay in truncated (connected) correlations. We give an expansion and use the symmetry to show that all terms vanish, except those displaying {\em replica condensation}. The condensation property ensures exponential tree decay. We illustrate our method in a low-temperature Ising system, but expect that one can use a similar method in other random field and quantum field problems. While considering the illustration, we prove an elementary upper bound on the entropy of random lattice surfaces.