Projects per year
Abstract
Recently, we argued [Chin. Phys. Lett. 39, 080502 (2022)0256-307X10.1088/0256-307X/39/8/080502] that the Ising model simultaneously exhibits two upper critical dimensions (dc=4,dp=6) in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a systematic study of the FK Ising model on hypercubic lattices with spatial dimensions d from 5 to 7, and on the complete graph. We provide a detailed data analysis of the critical behaviors of a variety of quantities at and near the critical points. Our results clearly show that many quantities exhibit distinct critical phenomena for 4<d<6 and d≥6, and thus strongly support the argument that 6 is also an upper critical dimension. Moreover, for each studied dimension, we observe the existence of two configuration sectors, two lengthscales, as well as two scaling windows, and thus two sets of critical exponents are needed to describe these behaviors. Our finding enriches the understanding of the critical phenomena in the Ising model.
| Original language | English |
|---|---|
| Article number | 044103 |
| Number of pages | 15 |
| Journal | Physical Review E |
| Volume | 107 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 7 Apr 2023 |
Projects
- 1 Finished
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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))
Australian Research Council (ARC), 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