Probability Seminar:Akira Sakai

The (lattice) phi^4 model is a scalar field-theoretical model that exhibits a phase transition. It is believed to be in the same universality class as the Ising model. In fact, we can construct the phi^4 model as the N --> infinity limit of the sum of N Ising systems (with the right scaling of spin-spin couplings). Using this Griffiths-Simon construction and applying the lace expansion for the Ising model, we can prove mean-field asymptotic behavior for the critical phi^4 two-point function. In this talk, I will explain the key points of the proof, and discuss possible extensions of the results to the power-law coupling case.