Simulation of a scalar field on a fuzzy sphere

Understand

The phi^4 real scalar field theory on a fuzzy sphere is studied numerically.

• We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a disordered phase, and a non-uniform ordered phase where the spatial SO(3) symmetry of the round sphere is spontaneously broken and which has no classical equivalent.
• The three coexistence lines between these phases, which meet at a triple point, are carefully located with particular attention paid to the one between the two ordered phases and the triple point itself.
• In the neighbourhood of the triple point all phase boundaries are well approximated by straight lines which, surprisingly, have the same scaling.