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.