Old and New Results on Multicritical Points

Amnon Aharony*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Thirty years after the Liu-Fisher paper on the bicritical and 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 decoupled fixed point is stable, implying a 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.

Original languageEnglish
Pages (from-to)659-669
Number of pages11
JournalJournal of Statistical Physics
Issue number3-6
StatePublished - Mar 2003


FundersFunder number
German-Israeli Foundation for Scientific Research and Development
United States-Israel Binational Science Foundation


    • Bicritical point
    • Decoupled fixed point
    • Multicritical points
    • Renormalization group
    • Tetracritical point


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