Old and new results on multicritical points

Details Old and new results on multicritical points Old and new results on multicritical points

2002-01-31

arxiv.org/abs/cond-mat/0201576v1

Physics

Condensed Matter

Statistical Mechanics

Paper presented at the December 2001 Rutgers meeting, celebrating Michael Fisher's 70th birthday

Scientific paper

Thirty years after the Liu-Fisher paper on the {\bf bicritical} and {\bf tetracritical} points in quantum lattice gases, these multicritical points continue to appear in a variety of new physical contexts. This paper reviews some recent multicritical phase diagrams, which involve e. g. high-$T_c$ superconductivity and various magnetic phases which may (or may not) coexist with it. One recent example concerns the SO(5) theory, which combines the 3-component antiferromagnetic and the 2-component superconducting order parameters. There, the competition between the isotropic, biconical and decoupled fixed points yields bicritical or tetracritical points. Recalling old results on the subject, it is shown that the {\bf decoupled} fixed point is stable, implying a {\bf tetracritical} point, contrary to recent claims, which are critically discussed. Other examples, concerning e. g. the superconducting versus charge and spin density wave phases are also discussed briefly. In all cases, extensions of old results can be used to correct new claims.

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