Geometric Explanation of Anomalous Finite-Size Scaling in High Dimensions

Jens Grimm, Eren Metin Elçi, Zongzheng Zhou, Timothy M. Garoni, Youjin Deng

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behavior for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.

Original languageEnglish
Article number115701
Number of pages5
JournalPhysical Review Letters
Issue number11
Publication statusPublished - 13 Mar 2017

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