Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2009-03-11
Int.J.Mod.Phys.A24:3917-3944,2009
Physics
High Energy Physics
High Energy Physics - Lattice
30 pages, 10 figures, accepted in International Journal of Modern Physics A
Scientific paper
10.1142/S0217751X09043195
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. We argue that unless an additional term is added to enhance the effect of the kinetic term the infinite matrix limit of this model will not correspond to a real scalar field on the commutative sphere or plane.
Flores Fernando García
Martin Xavier
O'Connor Denjoe
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