Unconventional critical behaviour in quantum systems with interactions decaying as a power law

Criticality of n-vector quantum systems is studied, via a renormalization group treatment, assuming a pair interaction which decays as a power law involving a characteristics parameter θ. Within a “single”-expansion parameter scheme for finite values of θ, a novel fixed point appears for nonbosonic systems both in the classical and quantum regimes and for bosonic ones only in the classical regime. Under certain conditions, it governs a new criticality which exhibits superuniversality with respect to the symmetry of the order parameter and absence of dimensional crossover. An interesting aspect of the formalism is that it allows us to investigate the critical properties of a wide class of systems at realistic dimensionalities suggesting new experimental possibilities. For infinitesimal values of θ, a “double”-expansion parameter scheme yields two new accessible fixed points which, surprisingly, control the same criticality with restored dimensional crossover for nonbosonic systems. For bosonic systems in the quantum regime, the long-range tail in the interaction induces a runaway which signals the absence of any sharp second-order transition in contrast with the usual short-range scenario.