1998/09/30 by O. Borisenko, V. Kushnir, A. Velytsky +1 · 7 citations
Mathematics · Physics and Astronomy · #Analogy #Geometry #Mathematical physics #Mathematics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Statistical physics #Symmetry (geometry) #Theoretical and Computational Physics #cond-mat #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.62.025013
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 62(2) (American Physical Society) · 20 pages, Latex, 1 fig. Typo in Eq.(46) which led to wrong result is corrected. Agreement with conventional method is recovered
arxiv created 1999/03/03 · openalex publication_date 2000/06/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.