Finite-Order Correlation Length for Four-Dimensional Weakly Self-Avoiding Walk and \({|\varphi|^4}\) Spins

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• 作者：Roland Bauerschmidt ; Gordon Slade ; Alexandre Tomberg…
• 刊名：Annales Henri Poincaré
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：18
• 期：2
• 页码：375-402
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Eleme
• 出版者：Springer International Publishing
• ISSN：1424-0661
• 卷排序：18

文摘

We study the four-dimensional n-component \({|\varphi|^4}\) spin model for all integers \({n \ge 1}\) and the four-dimensional continuous-time weakly self-avoiding walk which corresponds exactly to the case \({n=0}\) interpreted as a supersymmetric spin model. For these models, we analyse the correlation length of order p, and prove the existence of a logarithmic correction to mean-field scaling, with power \({\frac 12\frac{n+2}{n+8}}\), for all \({n \ge 0}\) and \({p > 0}\). The proof is based on an improvement of a rigorous renormalisation group method developed previously.