Phase structure of a three-dimensional Yukawa model

Abstract

We use the method of the exact renormalization group to study the renormalization group flows of an O(N) invariant Yukawa model in three dimensional Euclidean space consisting of one real scalar and N real spinor fields. We obtain a phase structure similar to that of the N-vector model with cubic anisotropy, possessing a region of parameters exhibiting a first order transition. The particular case with one real fermion (N=1) belongs to the same universality class as the Wess-Zumino model with one supersymmetry. For the critical exponents of the Wilson-Fisher type fixed points, our 1-loop approximations are generally consistent with the results of previous studies.

24 pages, 10 figures, formatted in PTP-TEX

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• Aspects of the Functional Renormalisation Group
• Optimisation of the exact renormalisation group
• Exact Renormalization Group Equations. An Introductory Review
• Critical exponents of the Gross-Neveu model from the effective average action
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• Critical $O(2)$ and $O(3)$ ${\varphi }^4$ theories near six dimensions
• Random-mass disorder in the critical Gross-Neveu-Yukawa models
• Limit of vanishing regulator in the functional renormalization group
• Three dimensional Yukawa models and CFTs at strong and weak couplings
• Critical Wess-Zumino models with four supercharges from the functional renormalization group