On the Yang-Lee and Langer singularities in the O(n) loop model

Details On the Yang-Lee and Langer singularities in the O(n) loop model On the Yang-Lee and Langer singularities in the O(n) loop model

2011-10-05

arxiv.org/abs/1110.1108v2

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 16 figures

Scientific paper

We use the method of `coupling to 2d QG' to study the analytic properties of the universal specific free energy of the O(n) loop model in complex magnetic field. We compute the specific free energy on a dynamical lattice using the correspondence with a matrix model. The free energy has a pair of Yang-Lee edges on the high-temperature sheet and a Langer type branch cut on the low-temperature sheet. Our result confirms a conjecture by A. and Al. Zamolodchikov about the decay rate of the metastable vacuum in presence of Liouville gravity and gives strong evidence about the existence of a weakly metastable state and a Langer branch cut in the O(n) loop model on a flat lattice. Our results are compatible with the Fonseca-Zamolodchikov conjecture that the Yang-Lee edge appears as the nearest singularity under the Langer cut.

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