The continuum limit of the non-commutative lambda phi^4 model
Abstract
We present a numerical study of the \lambda \phi^{4} model in three Euclidean dimensions, where the two spatial coordinates are non-commutative (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 non-commutativity parameter constant. The dispersion relation in the disordered phase stabilizes in this limit, which represents a non-perturbative renormalization. From its shape we infer that the striped phase persists in the continuum, and we observe UV/IR mixing as a non-perturbative effect.
Cite
@article{arxiv.hep-th/0407012,
title = {The continuum limit of the non-commutative lambda phi^4 model},
author = {W. Bietenholz and F. Hofheinz and J. Nishimura},
journal= {arXiv preprint arXiv:hep-th/0407012},
year = {2017}
}
Comments
3 pages, 3 figures, talk presented by W.B. at the 11th Regional Conference on Mathematical Physics, Tehran, May 3-6, 2004