Thermodynamics of the 1+1-dimensional nonlinear sigma model through next-to-leading order in 1/N

Abstract

We discuss the thermodynamics of the O(N) nonlinear sigma model in 1+1 dimensions. In particular we investigate the NLO 1/N correction to the 1PI finite temperature effective potential expressed in terms of an auxiliary field. The effective potential contains temperature-dependent divergences which cannot be renormalized properly. We argue that this problem vanishes at the minimum of the effective potential. Therefore physical quantities like the pressure are well defined and can be renormalized in a temperature-independent way. We give a general argument for the occurrence of temperature-dependent divergences outside the minimum. We present calculations of the pressure and show that 1/N is a good expansion. It turns out that the pressure normalized to that at infinite temperature is N-independent like the flavor independence of the same quantity in QCD.