Title: O(n) loops in complex magnetic field coupled to 2D gravity: Lee-Yang and Langer singularities
Speaker: Ivan Kostov, IPhT, Saclay
Date: Wednesday, April 24, 2013
Time: 2:00pm – 3:00pm
Place: Seminar Room 313, Simons Center
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Abstract: The $O(n)$ loop model on planar graphs is solved in presence of constant magnetic field H. The geometrical expansion involves (self and mutually avoiding) loops with fugacity $n$ and open lines with fugacity $H^2$. The universal specific 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 at $H=0$. The value of the exponent of the Langer type singularity is compatible with a conjecture by A. and Al. Zamolodchikov about the decay rate of the metastable vacuum in presence of Liouville gravity.