Noncommutative Field Theory: Numerical Analysis with the Fuzzy Disc

Understand

The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group.

• We define a $\varphi^4$ scalar field theory on it and analyze numerically for three different limits for the rank of the matrix going to infinity.
• The numerical simulations reveal three different phases: uniform and disordered phases already the present in the commutative scalar field theory and a nonuniform ordered phase as a noncommutative effects.
• We have computed the transition curves between phases and their scaling.