title: Ising (conformal) fields and cluster area measures.
abstract: We provide a representation for the scaling limit of the d = 2 critical Ising magnetization field as a (conformal) random field by 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.
authors.affiliation: Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands. fede@few.vu.nl
authors.forename: Federico
authors.initials: F
authors.lastname: Camia
authors.forename: Charles M
authors.initials: CM
authors.lastname: Newman