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Conformal measure ensembles and planar Ising magnetization: a review. (English) Zbl 1469.60311

Summary: We provide a review of results on the critical and near-critical scaling limit of the planar Ising magnetization field obtained in the past dozen years. The results are presented in the framework of coupled loop and measure ensembles, and some new proofs are provided.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B27 Critical phenomena in equilibrium statistical mechanics
81T27 Continuum limits in quantum field theory
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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