Our modern understanding of universality, namely the independence of the critical properties of a system from its microscopic details, is based on the ideas put forward by K. Wilson and formalised within the framework of the renormalization group (RG).

Despite the centrality of the subject in modern days theoretical physics, the classification of universality classes, both at and out of equilibrium, is to date largely unsolved.

We employ the functional perturbative RG within the ε-expansion scheme to study RG fixed points of scalar field theories endowed with the discrete symmetry groups of regular polytopes.

The main results of this analysis include a new candidate universality class in three physical dimensions based on the dihedral symmetry group D(5) of the Pentagon.

Reference: arXiv:1902.05328