O(n) vector model at n=-1, -2 on random planar lattices: a direct combinatorial derivation

Details O(n) vector model at n=-1, -2 on random planar lattices: a direct combinatorial derivation O(n) vector model at n=-1, -2 on random planar lattices: a direct combinatorial derivation

2004-12-13

arxiv.org/abs/cond-mat/0412327v2

J.Stat.Mech.0502:P02002,2005

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

10.1088/1742-5468/2005/02/P02002

The O(n) vector model with logarithmic action on a lattice of coordination 3 is related to a gas of self-avoiding loops on the lattice. This formulation allows for analytical continuation in n: critical behaviour is found in the real interval [-2,2]. The solution of the model on random planar lattices, recovered by random matrices, also involves an analytic continuation in the number n of auxiliary matrices. Here we show that, in the two cases n=-1, -2, a combinatorial reformulation of the loop gas problem allows to achieve the random matrix solution with no need of this analytical continuation.

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