The O(n) vector model at n = -1, -2 on random planar lattices: a direct combinatorial derivation
Articolo
Data di Pubblicazione:
2005
Citazione:
The O(n) vector model at n = -1, -2 on random planar lattices: a direct combinatorial derivation / S. Caracciolo, A. Sportiello. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2005:02(2005), pp. 135-142.
Abstract:
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 one to achieve the random matrix solution with no need of this analytical continuation.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
loop models and polymers; solvable lattice models
Elenco autori:
S. Caracciolo, A. Sportiello
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