Replica Condensation and Tree Decay

Details Replica Condensation and Tree Decay Replica Condensation and Tree Decay

2007-06-14

arxiv.org/abs/0706.2147v1

Physics

Mathematical Physics

Scientific paper

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.

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