Low-Temperature Behaviour of 2D Lattice SU(2) Spin Model

Abstract

A dual representation for the two-dimensional lattice SU(2) principal chiral model is constructed in the region of large angular momenta. Using one approximation and one assumption we calculate the low-temperature asymptotics of the two-point correlation function and prove that it has a power-like decay. The approximation consists in substituting the SU(2) matrix elements by their asymptotics which hold uniformly in the vicinity of the identity element of the SU(2) link matrix. Besides, we assume that certain local defects cannot be responsible for the mass gap generation. Our result implies that the model cannot be asymptotically free.