  In this paper we demonstrate that coordinate noncommutativity at short
distances can show up in critical phenomena through UV-IR mixing. In the
symmetric phase of the Landau-Ginsburg model, noncommutativity is shown to give
rise to a non-zero anomalous dimension at one loop, and to cause instability
towards a new phase at large noncommutativity. In particular, in less than four
dimensions, the one-loop critical exponent $\eta$ is non-vanishing at the
Wilson-Fisher fixed point.
