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 .
"A tightness criterion for random fields, with application to the Ising model." Electron. J. Probab. 22 1 - 29, 2017. https://doi.org/10.1214/17-EJP121