Application of the lace expansion to the \(\varphi^4\) model

DOI10.1007/s00220-014-2256-xzbMath1315.82006arXiv1403.5714OpenAlexW2189403007MaRDI QIDQ2018301

Akira Sakai

Publication date: 14 April 2015

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5714

zbMATH Keywords

\(\phi^4\) modellace expansionSchwinger-Dyson equationGriffiths-Simon constructionIsing-model

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (10)

Lace expansion for dummies ⋮ Correct bounds on the Ising lace-expansion coefficients ⋮ The near-critical two-point function and the torus plateau for weakly self-avoiding walk in high dimensions ⋮ The scaling limit of the weakly self-avoiding walk on a high-dimensional torus ⋮ A survey on the lace expansion for the nearest-neighbor models on the BCC lattice ⋮ Critical exponents for long-range \(\mathrm O(n)\) models below the upper critical dimension ⋮ Mean-Field Bound on the 1-Arm Exponent for Ising Ferromagnets in High Dimensions ⋮ Critical two-point function for long-range models with power-law couplings: the marginal case for \({d\ge d_{\mathrm{c}}}\) ⋮ A simple convergence proof for the lace expansion ⋮ Critical correlation functions for the 4-dimensional weakly self-avoiding walk and \(n\)-component \(|\varphi|^4\) model

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