Scalar fields in a non-commutative space

Understand

We discuss the lambda phi**4 model in 2- and 3-dimensional non-commutative spaces.

• The mapping onto a Hermitian matrix model enables its non-perturbative investigation by Monte Carlo simulations.
• The numerical results reveal a phase where stripe patterns dominate.
• In d=3 we show that in this phase the dispersion relation is deformed in the IR regime, in agreement with the property of UV/IR mixing.