A tightness criterion for random fields, with application to the Ising model. (English) Zbl 1378.60065

Furlan, Marco; Mourrat, Jean-Christophe

Electron. J. Probab. 22, Paper No. 97, 29 p. (2017).

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

Keywords:

tightness criterion; local Besov spaces; Ising model

Citations:

Zbl 1332.82012