1996/05/14 by Guillermo E. Castilla, G. E. Castilla, S. Chakravarty +1
Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1016/s0550-3213(96)00617-7
published as Nucl.Phys. B485 (1997) 613-645 · RevTex, 33 pages, figures embedded
arxiv created 1996/05/14 · openalex publication_date 1997/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Nonlinear σ-model is an ubiquitous model. In this paper, the O(N) model where the N-component spin is a unit vector, \bf S2=1,is considered. The stability of this model with respect to gradient operators (∂μ\bf S⋅ ∂ν\bf S)s, where the degree s is arbitrary, is discussed. Explicit two-loop calculations within the scheme of ε-expansion, where ε=(d-2), leads to the surprising result that these operators are relevant. In fact, the relevancy increases with the degree s. We argue that this phenomenon in the O(N)-model actually reflects the failure of the perturbative analysis, that is, the (2+ε)-expansion. It is likely that it is necessary to take into account non-perturbative effects if one wants to describe the phase transition of the Heisenberg model within the context of the non-linear σ-model. Thus, uncritical use of the (2+ε)-expansion may be misleading, especially for those cases for which there are not many independent checks.