At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.
Analytical Solutions of Exact Renormalization Group Equations
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We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second order phase transitions, critical exponents, first order transitions (some of which are radiatively induced) and tricritical behaviour.
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Fermions and the Renormalisation Group at Large N
At large N, fermionic quantum field theories have exact effective actions depending only on flavour-singlet fermion bilinears, making the local potential approximation exact and yielding new conformal fixed points.