Journal Article Application of the Lace Expansion to the φ4 Model

Sakai, Akira

336 ( 2 )  , pp.619 - 648 , 2015-06-01 , Springer
Using the Griffiths–Simon construction of the φ4 model and the lace expansion for the Ising model, we prove that, if the strength λ≥0 of nonlinearity is sufficiently small for a large class of short-range models in dimensions d > 4, then the critical φ4 two-point function ⟨φoφx⟩μc is asymptotically |x|2−d times a model-dependent constant, and the critical point is estimated as μc=J^−λ2⟨φ2o⟩μc+O(λ2) , where J^ is the massless point for the Gaussian model.

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