Multi-meson Yukawa interactions at criticality

The critical behavior of a relativistic $\mathbb{Z}_2$-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 multi-meson 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 four-dimensional high-energy models or in lower-dimensional condensed-matter systems. By means of the latter method, we describe the generation of multi-critical models in less then three dimensions, both at infinite and finite number 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.