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.
| Original language | English |
|---|---|
| Article number | 115701 |
| Number of pages | 5 |
| Journal | Physical Review Letters |
| Volume | 118 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 13 Mar 2017 |
Projects
- 2 Finished
-
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights
Hall, P. (Primary Chief Investigator (PCI)), Bartlett, P. (Chief Investigator (CI)), Bean, N. (Chief Investigator (CI)), Burrage, K. (Chief Investigator (CI)), DeGier, J. (Chief Investigator (CI)), Delaigle, A. (Chief Investigator (CI)), Forrester, P. (Chief Investigator (CI)), Geweke, J. (Chief Investigator (CI)), Kohn, R. (Chief Investigator (CI)), Kroese, D. (Chief Investigator (CI)), Mengersen, K. L. (Chief Investigator (CI)), Pettit, A. (Chief Investigator (CI)), Pollett, P. (Chief Investigator (CI)), Roughan, M. (Chief Investigator (CI)), Ryan, L. M. (Chief Investigator (CI)), Taylor, P. (Chief Investigator (CI)), Turner, I. (Chief Investigator (CI)), Wand, M. (Chief Investigator (CI)), Garoni, T. (Chief Investigator (CI)), Smith-Miles, K. A. (Chief Investigator (CI)), Caley, M. (Partner Investigator (PI)), Churches, T. (Partner Investigator (PI)), Elazar, D. (Partner Investigator (PI)), Gupta, A. (Partner Investigator (PI)), Harch, B. (Partner Investigator (PI)), Tam, S.-M. (Partner Investigator (PI)), Weegberg, K. (Partner Investigator (PI)), Willinger, W. (Partner Investigator (PI)) & Hyndman, R. (Chief Investigator (CI))
ARC - Australian Research Council, Monash University – Internal Department Contribution, University of Melbourne, Queensland University of Technology (QUT), University of Adelaide, University of New South Wales (UNSW), University of Queensland , University of Technology (UTS) Sydney, Monash University – Internal University Contribution, Monash University – Internal Faculty Contribution, Monash University – Internal School Contribution, Roads Corporation (trading as VicRoads) (Victoria)
1/01/17 → 31/12/21
Project: Research
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Finite Markov chains in statistical mechanics and combinatorics
Garoni, T. (Primary Chief Investigator (PCI)), Collevecchio, A. (Chief Investigator (CI)) & Markowsky, G. (Chief Investigator (CI))
ARC - Australian Research Council
2/01/14 → 31/12/17
Project: Research
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