Coupier, David; Doukhan, Paul; Ycart, Bernard Zero-one laws for binary random fields. (English) Zbl 1104.60017 ALEA, Lat. Am. J. Probab. Math. Stat. 2, 157-175 (2006). Summary: A set of binary random variables indexed by a lattice torus is considered. Under a mixing hypothesis, the probability of any proposition belonging to the first-order logic of colored graphs tends to 0 or 1, as the size of the lattice tends to infinity. For the particular case of the Ising model with bounded pair potential and surface potential tending to \(-\infty\), the threshold functions of local propositions are computed, and sufficient conditions for the zero-one law are given. Cited in 4 Documents MSC: 60F20 Zero-one laws 60K35 Interacting random processes; statistical mechanics type models; percolation theory PDFBibTeX XMLCite \textit{D. Coupier} et al., ALEA, Lat. Am. J. Probab. Math. Stat. 2, 157--175 (2006; Zbl 1104.60017) Full Text: arXiv