Study of the Kosterlitz-Thouless transition by the Mayer expansion

Abstract

The Kosterlitz-Thouless transition in the 2D U(1) σ- or XY-model is studied by the Mayer expansion through the duality transformation. If the inverse temperature β is large, the pressure and the two-point function 〈 cos( θ 0 − θ ζ )〉 are given by Σ ∞ 2 a N ( β) and exp[( 2 β )C 0(ζ) + Σ ∞ 2b N(β;ζ)] respectively. Here C 0( ζ) = -(2 π) -1log(∣ ζ∣ + 1), (i) | a N ( β) ∣ ⩽ C 1( N) × exp[- βK 1 N], ( ii) ∣ b N ( β; ζ)∣ ⩽ C 2( N) exp[- βK 2 N]∣ C 0( ζ)∣, K i > 0. Each term is divergent for β < β c . The series seems to be absolutely convergent for β > β′ c .