Abstract
We use the method of ‘coupling to 2d QG’ to study the analytic properties of the universal specific free energyof the O(n) loop model in a complex magnetic field. We compute the specific free energy on adynamical lattice using the correspondence with a matrix model. The free energyhas a pair of Yang–Lee edges on the high-temperature sheet and a Langer-typebranch cut on the low-temperature sheet. Our result confirms a conjecture byA Zamolodchikov and Al Zamolodchikov about the decay rate of the metastablevacuum in the presence of Liouville gravity and gives strong evidence aboutthe existence of a weakly metastable state and a Langer branch cut in theO(n) loop model on a flat lattice. Our results are compatible with the Fonseca–Zamolodchikovconjecture that the Yang–Lee edge appears as the nearest singularity under the Langercut.
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