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تسجيل مستخدم جديدApplication of the lace expansion to the $varphi^4$ model
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تأليف
Akira Sakai
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Using the Griffiths-Simon construction of the $varphi^4$ model and the lace expansion for the Ising model, we prove that, if the strength $lambdage0$ of nonlinearity is sufficiently small for a large class of short-range models in dimensions $d>4$, then the critical $varphi^4$ two-point function $langlevarphi_ovarphi_xrangle_{mu_c}$ is asymptotically $|x|^{2-d}$ times a model-dependent constant, and the critical point is estimated as $mu_c=mathscr{hat J}-fraclambda2langlevarphi_o^2rangle_{mu_c}+O(lambda^2)$, where $mathscr{hat J}$ is the massless point for the Gaussian model.
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