Importance of the topological defects for two dimensional phase transitions and their relevance for the renormalization group

Abstract

For various two dimensional non linear $\sigma$ models, we present a direct comparison between the $\beta$ functions computed with the $2+\epsilon$ renormalization group and the $\beta$ functions measured by Monte Carlo simulations. The theoretical and measured $\beta$ functions match each other nicely for models with a trivial topology, yet they disagree clearly for models containing topological defects. In these later cases, they are compatible with a phase transition at a finite temperature. This indicates that the global properties of the manifold do matter, in contradiction with the assumption used in the $2+\epsilon$ RG computation.

RevTex file, 8 pages, to appears in Phys.Lett.A

References in corpus (2)

• A Renormalization Group Study of Helimagnets in D=2+EPSILON Dimensions
• New Universality Classes for Two-Dimensional $\sigma$-Models

Cited by in corpus (3)

• The critical behavior of 2-d frustrated spin models with noncollinear order
• High-gradient operators in the N-vector model
• Weak first-order transition in the quasi-one-dimensional frustrated XY antiferromagnet