Metastability of the Ising model on random regular graphs at zero temperature

Dommers, Sander

Abstract

We study the metastability of the ferromagnetic Ising model on a random r-regular graph in the zero temperature limit. We prove that in the presence of a small positive external field the time that it takes to go from the all minus state to the all plus state behaves like exp(β(r/2+O(r√))n) when the inverse temperature β→∞ and the number of vertices n is large enough but fixed. The proof is based on the so-called pathwise approach and bounds on the isoperimetric number of random regular graphs.

Citation

Dommers, S. (2017). Metastability of the Ising model on random regular graphs at zero temperature. Probability theory and related fields, 167(1-2), 305-324. https://doi.org/10.1007/s00440-015-0682-0

• Journal Article Type: Article
• Acceptance Date: Nov 25, 2014
• Online Publication Date: Nov 28, 2015
• Publication Date: Feb 1, 2017
• Deposit Date: Jun 29, 2018
• Journal: Probability Theory and Related Fields
• Print ISSN: 0178-8051
• Electronic ISSN: 1432-2064
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 167
• Issue: 1-2
• Pages: 305-324
• DOI: https://doi.org/10.1007/s00440-015-0682-0
• Keywords: Metastability; Ising model; Random graphs; Pathwise approach
• Public URL: https://hull-repository.worktribe.com/output/900202
• Publisher URL: https://link.springer.com/article/10.1007/s00440-015-0682-0