MenuMathematical Physics and Harmonic Analysis Seminar
Date: February 3, 2017
Time: 1:50PM - 2:50PM
Location: BLOC 220
Speaker: Prof. Vitaly Kocharovsky, Texas A&M, Physics
Title: Permanents of circulant and degenerate Schur matrices for the solution to 3D Ising model
Abstract: The goal of this talk is to discuss an open fundamental problem of finding the asymptotics of the permanent of circulant matrix. A solution to this mathematical problem would be tremendously important for physics of many-body systems and critical phenomena, as well as for quantum field theory. We present three exact formulas for the permanents of circulant and degenerate Schur matrices. These combinatorial and integral formulas are intended for the analytical and asymptotic evaluation of the circulant-matrix permanents needed for the solution to 3D Ising model. References 1.V.V. Kocharovsky, Vl.V. Kocharovsky, Exact general solution to the three-dimensional Ising model and a self-consistency equation for the nearest-neighbors' correlations, arXiv:cond-mat.stat-mech/1510.07327v3 24Mar2016. 2.V.V. Kocharovsky, Vl.V. Kocharovsky, Microscopic theory of phase transitions in a critical region, Physica Scripta 90, 108002 (2015). 3.V.V. Kocharovsky, Vl.V. Kocharovsky, Towards an exact solution for the three-dimensional Ising model: A method of the recurrence equations for partial contractions, Phys. Lett. A 379, 2520 (2015). 4.V.V. Kocharovsky, Vl.V. Kocharovsky, Microscopic theory of a phase transition in a critical region: Bose-Einstein condensation in an interacting gas, Phys. Lett. A 379, 466 (2015). 5.V.V. Kocharovsky, Vl.V. Kocharovsky, S.V. Tarasov, Bose-Einstein condensation in the mesoscopic systems: Self-similar structure of the critical region and nonequivalence of the canonical and grand canonical ensembles, JETP Letters, 103, 62-75 (2016).
