Surface order large deviations for Ising, Potts and percolation models
We derive uniform surface order large deviation estimates for the block magnetization in finite volume Ising (or Potts) models with plus or free (or a combination of both) boundary conditions in the phase coexistence regime for \(d\geq 3\). The results are valid up to a limit of slab-thresholds, conjectured to agree with the critical temperature. Our arguments are based on the renormalization of the random cluster model with \(q\geq 1\) and \(d\geq 3\), and on corresponding large deviation estimates for the occurrence in a box of the largest cluster with density close to the percolation probability. The results are new even for the case of independent percolation \((q=1)\). As a byproduct of our methods, we obtain further results in the FK model concerning semicontinuity (in \(p\) and \(q\)) of the percolation probability, the second largest cluster in a box and the tail of the finite cluster size distribution.
scientific article; zbMATH DE number 878013
scientific article