# Replica Condensation and Tree Decay - Mathematical Physics

Abstract: We give an intuitive method-using local, cyclic replica symmetry-to isolateexponential tree decay in truncated connected correlations. We give anexpansion and use the symmetry to show that all terms vanish, except thosedisplaying {\em replica condensation}. The condensation property ensuresexponential tree decay.We illustrate our method in a low-temperature Ising system, but expect thatone can use a similar method in other random field and quantum field problems.While considering the illustration, we prove an elementary upper bound on theentropy of random lattice surfaces.

Author: Arthur Jaffe, David Moser

Source: https://arxiv.org/