The Continuum Limit of the Noncommutative λϕ^{4} Model
Abstract
We present a numerical study of the λϕ^{4} 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.
 Publication:

Mathematical Physics
 Pub Date:
 April 2005
 DOI:
 10.1142/9789812701862_0045
 arXiv:
 arXiv:hepth/0407012
 Bibcode:
 2005maph.conf..169B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 3 pages, 3 figures, talk presented by W.B. at the 11th Regional Conference on Mathematical Physics, Tehran, May 36, 2004