Phase transition and critical behaviour of the d=3 Gross-Neveu model

Abstract

A second order phase transition for the three dimensional Gross-Neveu model is established for one fermion species N=1. This transition breaks a paritylike discrete symmetry. It constitutes its peculiar universality class with critical exponent ν= 0.63 and scalar and fermionic anomalous dimension η_σ= 0.31 and η_ψ= 0.11, respectively. We also compute critical exponents for other N. Our results are based on exact renormalization group equations.

4 pages, 1 figure; v4 corresponds to the published article

References in corpus (3)

• Exact evolution equation for the effective potential
• Optimised Renormalisation Group Flows
• Renormalization Flow of Bound States

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