## Abstract

We consider the Z_{2} 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/π^{2}N + O(1/N^{2}) and is therefore irrelevant. The generalization to universality classes corresponding to breakdown of larger chiral groups is discussed.

Original language | English |
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Pages (from-to) | 76-98 |

Number of pages | 23 |

Journal | Nuclear Physics, Section B |

Volume | 385 |

Issue number | 1-2 |

DOIs | |

State | Published - 19 Oct 1992 |