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

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

1996-01-30

arxiv.org/abs/cond-mat/9601147v1

J. Phys. A: Math. Gen. 29 (1996) 5333.

Physics

Condensed Matter

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

Scientific paper

10.1088/0305-4470/29/17/010

We solve $O(n,1)$ nonlinear vector model on Bethe lattice and show that it exhibits a transition from ordered to disordered state for $0 \leq n < 1$. 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.

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