Finite-size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

The ground state and low-T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite-volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite-size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T = 0 critical point.