Abstract
We present a non-perturbative study of the λϕ 4 model on a non-commutative plane. The lattice regularised form can be mapped onto a Hermitian matrix model, which enables Monte Carlo simulations. Numerical data reveal the phase diagram; at large λ it contains a “striped phase”, which is absent in the commutative case. We explore the question whether or not this phenomenon persists in a Double Scaling Limit (DSL), which extrapolates simultaneously to the continuum and to infinite volume, at a fixed non-commutativity parameter. To this end, we introduce a dimensional lattice spacing based on the decay of the correlation function. Our results provide evidence for the existence of a striped phase even in the DSL, which implies the spontaneous breaking of translation symmetry. Due to the non-locality of this model, this does not contradict the Mermin-Wagner theorem.
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Mejía-Díaz, H., Bietenholz, W. & Panero, M. The continuum phase diagram of the 2d non-commutative λϕ 4 model. J. High Energ. Phys. 2014, 56 (2014). https://doi.org/10.1007/JHEP10(2014)056
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DOI: https://doi.org/10.1007/JHEP10(2014)056