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

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

1995-04-11

arxiv.org/abs/cond-mat/9504045v2

Physics

Condensed Matter

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

Scientific paper

10.1016/0375-9601(95)00177-5

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.

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