Low-temperature expansion and perturbation theory in 2D models with unbroken symmetry: A new approach

A new method for constructing weak coupling expansion of two-dimensional models with an unbroken continuous symmetry is developed. The method is based on an analogy with the Abelian XY model, respects the Mermin-Wagner theorem, and uses a link representation of the partition and correlation functions. An expansion of the free energy and of the correlation functions at small temperatures is performed and first order coefficients are calculated explicitly. They are proved to be path independent and infrared finite. We also study the free energy of the one-dimensional SU(N) model and demonstrate a nonuniformity of the low-temperature expansion in the volume for this system. Further, we investigate the contribution of holonomy operators to the low-temperature expansion in two dimensions and show that they do not survive the large volume limit. All our results agree with the conventional expansion. We discuss the applicability of our method to analysis of the uniformity of the low-temperature expansion in two dimensions.