Scaling limits for weakly pinned Gaussian random fields under the   presence of two possible candidates
  We study the scaling limit and prove the law of large numbers for weakly pinned Gaussian random fields under the critical situation that two possible candidates of the limits exist at the level of large deviation principle. This paper extends the results of [3], [7] for one dimensional fields to higher dimensions: d \geq 3, at least if the strength of pinning is sufficiently large. 
Erwin Bolthausen, Taizo Chiyonobu, Tadahisa Funaki
math.PR