Multimeson Yukawa interactions at criticality

The critical behavior of a relativistic Z(2)-symmetric Yukawa model at zero temperature and density is discussed for a continuous number of fermion degrees of freedom and of spacetime dimensions, with emphasis on the role played by multimeson exchange in the Yukawa sector. We argue that this should be generically taken into account in studies based on the functional renormalization group, either in fourdimensional high-energy models or in lower-dimensional condensed-matter systems. By means of the latter method, we describe the generation of multicritical models in less than three dimensions, both at infinite and finite numbers of flavors. We also provide different estimates of the critical exponents of the chiral Ising universality class in three dimensions for various field contents, from a couple of massless Dirac fermions down to the supersymmetric theory with a single Majorana spinor.