Colloque des sciences mathématiques du Québec

30 novembre 2007 de 16 h 00 à 18 h 00 (heure de Montréal/Miami) Sur place

Exact Solution of the Six-Vertex Model of Statistical Physics

Colloque par Pavel Bleher (Indiana University-Purdue University Indianapolis)

We prove the conjecture of Zinn-Justin that the partition function of the six-vertex model on the $N\times N$ lattice with domain wall boundary conditions has the asymptotics, $Z_N\sim  CN^\kappa e^{N^2}f$ as $N\to \infty$, and we find the exact value of the exponent $\kappa$. The solution is based on the Riemann-Hilbert approach and the Deift-Zhou nonlinear steepest descent method.

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