We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) randomfieldby using Schramm-Loewner Evolution clusters and associated renormalized area measures. The renormalized areas are from the scaling limit of the critical Fortuin-Kasteleyn clusters and the random field is a convergent sum of the area measures with random signs. Extensions to off-critical scaling limits, to d = 3, and to Potts models are also considered.
|Number of pages||17|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|Publication status||Published - 2009|