Geometric Explanation of Anomalous Finite-Size Scaling in High Dimensions

Jens Grimm, Eren Metin Elçi, Zongzheng Zhou, Timothy M. Garoni, and Youjin Deng
Phys. Rev. Lett. 118, 115701 – Published 13 March 2017

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 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.

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  • Received 7 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.115701

© 2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jens Grimm1, Eren Metin Elçi2, Zongzheng Zhou1, Timothy M. Garoni1, and Youjin Deng3

  • 1ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia
  • 2School of Mathematical Sciences, Monash University, Clayton, Victoria 3800, Australia
  • 3Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China and CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

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Issue

Vol. 118, Iss. 11 — 17 March 2017

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