A New Method for Proving the Existence of Phase Transitions
Rick Durrett · Birkhäuser Boston eBooks · 1991
In this paper we will describe a new method for proving the existence of phase transitions, developed in joint work with Maury Bramson, and apply it to four examples. The material here is related to Ted Harris’ work in at least four ways. First, all four examples are related to the contact process, a system he invented in 1974. Second, the method we are going to describe was used in his 1974 paper to show that the contact process has a phase transition. Third, all of our processes are constructed from Poisson processes using either the procedure he invented in 1972 for general finite range models or the graphical representations he invented for the contact process and related systems in 1978. Finally, branching processes play an important role in the proofs below.