The continuum limit of the non-commutative lambda phi^4 model

Details The continuum limit of the non-commutative lambda phi^4 model The continuum limit of the non-commutative lambda phi^4 model

2004-07-02

arxiv.org/abs/hep-th/0407012v1

Physics

High Energy Physics

High Energy Physics - Theory

3 pages, 3 figures, talk presented by W.B. at the 11th Regional Conference on Mathematical Physics, Tehran, May 3-6, 2004

Scientific paper

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.

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