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 $T_c(Q=0)$ is strictly greater than $\lim_{Q\to 0} T_c(Q)$. The behavior of this system at temperatures less than $T_c(Q=0)$ 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.