Multicritical hypercubic models

We study renormalization group multicritical fixed points in the epsilon-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group H-N. After reviewing the algebra of H-N-invariant polynomials and arguing that there can be an entire family of multicritical (hyper)cubic solutions with phi(2n) interactions in d = 2n/n-1 - epsilon dimensions, we use the general multicomponent beta functionals formalism to study the special cases d = 3 - epsilon and d = 8/3- epsilon, deriving explicitly the beta functions describing the flow of three- and four-critical (hyper)cubic models. We perform a study of their fixed points, critical exponents and quadratic deformations for various values of N, including the limit N = 0, that was reported in another paper in relation to the randomly diluted single-spin models, and an analysis of the large N limit, which turns out to be particularly interesting since it depends on the specific multicriticality. We see that, in general, the continuation in N of the random solutions is different from the continuation coming from large-N, and only the latter interpolates with the physically interesting cases of low- N such as N = 3. Finally, we also include an analysis of a theory with quintic interactions in d = 10/3 - epsilon and, for completeness, the NNLO computations in d = 4 - epsilon.

Automated summary

In this study, renormalization group multicritical fixed points in scalar field theories with symmetry of the (hyper)cubic point group H-N are investigated using the epsilon-expansion. Special cases in dimensions d = 3 - epsilon and d = 8/3- epsilon are analyzed, with explicit derivation of beta functions describing the flow of three- and four-critical (hyper)cubic models. The study includes an analysis of fixed points, critical exponents, and quadratic deformations for various values of N, revealing differences between the continuation in N of random solutions and the continuation from large N.