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arXiv · 1612.01722

Geometric explanation of anomalous finite-size scaling in high dimensions

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

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 behaviour for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.

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Jens Grimm, Eren Metin Elçi, Zongzheng Zhou, Timothy M. Garoni, Youjin Deng. 2017-03-15. Geometric explanation of anomalous finite-size scaling in high dimensions. https://doi.org/10.1103/physrevlett.118.115701

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