Paper
Percolation of both signs in a triangular-type 3D Ising model above $T_c$
Authors
Jianping Jiang, Sike Lang
Abstract
Let be the two-dimensional triangular lattice, and the one-dimensional integer lattice. Let denote the Cartesian product graph. Consider the Ising model defined on this graph with inverse temperature and external field , and let be the critical inverse temperature when . We prove that for each , there exists such that both a unique infinite cluster and a unique infinite cluster coexist whenever . The same coexistence result also holds for the three-dimensional triangular lattice.