Fixed points in frustrated magnets revisited

Details Fixed points in frustrated magnets revisited Fixed points in frustrated magnets revisited

2008-03-31

arxiv.org/abs/0803.4400v1

J. Stat. Mech. (2008) P03014

Physics

Condensed Matter

Statistical Mechanics

18 pages, 8 figures. This article is an extended version of arXiv:cond-mat/0609285

Scientific paper

10.1088/1742-5468/2008/03/P03014

We analyze the validity of perturbative renormalization group estimates obtained within the fixed dimension approach of frustrated magnets. We reconsider the resummed five-loop beta-functions obtained within the minimal subtraction scheme without epsilon-expansion for both frustrated magnets and the well-controlled ferromagnetic systems with a cubic anisotropy. Analyzing the convergence properties of the critical exponents in these two cases we find that the fixed point supposed to control the second order phase transition of frustrated magnets is very likely an unphysical one. This is supported by its non-Gaussian character at the upper critical dimension d=4. Our work confirms the weak first order nature of the phase transition occuring at three dimensions and provides elements towards a unified picture of all existing theoretical approaches to frustrated magnets.

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