The Continuum Limit of the Noncommutative λϕ4 Model

We present a numerical study of the λϕ⁴ model in three Euclidean dimensions, where the two spatial coordinates are noncommutative (NC). We first show the explicit phase diagram of this model on a lattice. The ordered regime splits into a phase of uniform order and a "striped phase". Then, we discuss the dispersion relation, which allows us to introduce a dimensionful lattice spacing. Thus, we can study a double scaling limit to zero lattice spacing and infinite volume, which keeps the noncommutativity parameter constant. The dispersion relation in the disordered phase stabilizes in this limit, which represents a nonperturbative renormalization. From its shape, we infer that the striped phase persists in the continuum, and we observe UV/IR mixing as a nonperturbative effect.