Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice and the Replica Limit

Abstract

We solve $O(n,1)$ nonlinear vector model on Bethe lattice and show that it exhibits a transition from ordered to disordered state for $0\le n<1$. If the replica limit $n\to 0$ is taken carefully, the model is shown to reduce to the corresponding supersymmetric model. The latter was introduced by Zirnbauer as a toy model for the Anderson localization transition. We argue thus that the non-compact replica models describe correctly the Anderson transition features. This should be contrasted to their failure in the case of the level correlation problem.

21 pages, REVTEX, 2 Postscript figures, uses epsf style

References in corpus (2)

• Distribution of local density of states in disordered metallic samples: logarithmically normal asymptotics
• On the localization transition in three dimensions: Monte-Carlo simulation of a non-linear $\sigma$-model

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• Conductance and its universal fluctuations in the directed network model at the crossover to the quasi-one-dimensional regime
• Equations of motion approach to the spin-1/2 Ising model on the Bethe lattice
• Non-linear sigma models on constant curvature target manifolds: a functional renormalization group approach