Interacting relativistic fermion systems play a role in high energy physics as effective models for weak interaction and chiral symmetry breaking in strong interaction, as toy model for asymptotically free models and simple realizations of asymptotically safe quantum field theories. In condensed matter they model the behaviour of Dirac-type materials like graphene for low electronic excitation energies. In a first part recent results on inhomogeneous chiral condensate in 2 dimensions at finite temperature, fermion density and flavour number are presented. In a second part we answer the question about the critical flavour number in 3 dimensional Thirring models. This number has been disputed over the past 28 years.