Numerical Study of Scalar Field Theory on the Fuzzy Onion

Abstract

We study the behaviour of the scalar field theory on the fuzzy onion model -- a three-dimensional matrix model consisting of concentric fuzzy spheres of gradually increasing radii. We use a numerical method of Hamiltonian Monte Carlo simulations to study the phase structure of this theory. We identify the field phases, investigate and describe a phenomenon of dynamical phase transitions and attempt to reconstruct phase transition lines. We compare the results with the well-studied phase structure of the fuzzy sphere. Finally, we identify two boundaries on the phase transitions of the theory, a uniform phase boundary and a critical boundary between the disordered and non-uniform phase.