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A tightness criterion for random fields, with application to the Ising model. (English) Zbl 1378.60065
Summary: We present a criterion for a family of random distributions to be tight in local Hölder and Besov spaces of possibly negative regularity on general domains. We then apply this criterion to find the sharp regularity of the magnetization field of the two-dimensional Ising model at criticality, answering a question of F. Camia et al. [Ann. Probab. 43, No. 2, 528–571 (2015; Zbl 1332.82012)].

MSC:
60F17 Functional limit theorems; invariance principles
60G60 Random fields
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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