Chiral phase transitions in d = 3 and renormalizability of four-Fermi interactions

G. Gat*, A. Kovner, Rosenstein Baruch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


We consider the Z2 chiral phase transition in 2 + 1 dimensions. It is shown that the infrared fixed point defining this universality class is the critical four-Fermi interaction theory. We calculate, using 1/N expansion, the UV dimension of various local operators. It is found that the fermionic mass and four-Fermi interaction operators are relevant with UV dimensions 1 + O(1/N) and 2 + O(1/N), respectively. This is the reason behind the non-perturbative renormalizability of four-Fermi interaction theories. The six-Fermi operator has dimension 3 + 8/π2N + O(1/N2) and is therefore irrelevant. The generalization to universality classes corresponding to breakdown of larger chiral groups is discussed.

Original languageEnglish
Pages (from-to)76-98
Number of pages23
JournalNuclear Physics, Section B
Issue number1-2
StatePublished - 19 Oct 1992

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