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arXiv · 1403.5714

Application of the lace expansion to the $φ^4$ model

Akira Sakai
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Abstract

Using the Griffiths-Simon construction of the $φ^4$ model and the lace expansion for the Ising model, we prove that, if the strength $λ\ge0$ of nonlinearity is sufficiently small for a large class of short-range models in dimensions $d>4$, then the critical $φ^4$ two-point function $\langleφ_oφ_x\rangle_{μ_c}$ is asymptotically $|x|^{2-d}$ times a model-dependent constant, and the critical point is estimated as $μ_c=\mathscr{\hat J}-\frac\lambda2\langleφ_o^2\rangle_{μ_c}+O(λ^2)$, where $\mathscr{\hat J}$ is the massless point for the Gaussian model.

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Akira Sakai. 2018-03-16. Application of the lace expansion to the $φ^4$ model. https://doi.org/10.1007/s00220-014-2256-x

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