A dimensionless Hamiltonian of an N-spin Ising model without an external magnetic field (Fig. 1a) is given by Figure 1: Ising model and set-up for generating artificial Ising spins based on DOPOs ...

Say that a graph has persistent transition if the Ising model on the graph can exhibit a phase transition (nonuniqueness of Gibbs measures) in the presence of a nonzero external field. We show that ...

They divided critical phenomena into classes with similar critical behavior. I also study the crucial role of the Lenz-Ising model in the development and justification of these ideas.