Critical two-point function for the \(\varphi^4\) model in dimensions \(d>4\)
The (lattice) \(\varphi^4\) 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 \(\varphi^4\) model as
the \(N\to\infty\) 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 \(\varphi^4\) 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.