Avoided critical behavior in a uniformly frustrated system

We study the effects of weak long-ranged antiferromagnetic interactions of strength Q on a spin model with predominant short-ranged ferromagnetic interactions. In three dimensions, this model exhibits an avoided critical point in the sense that the critical temperature Tc(Q = 0) is strictly greater than limQ→0Tc(Q). The behavior of this system at temperatures less than Tc(Q = 0) is controlled by the proximity to the avoided critical point. We also quantize the model in a novel way to study the interplay between charge-density wave and superconducting order.