Three-dimensional antiferromagnetic CP models

We investigate the critical behavior of three-dimensional antiferromagnetic CP (ACP) models in cubic lattices, which are characterized by a global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-GinzburgWilson (LGW) model. For N = 3 this mapping allows us to conclude that the three-component ACP model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N ≥ 4. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.