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

Dommers, Sander

Authors

Dr Sander Dommers S.Dommers@hull.ac.uk
Lecturer in Statistics, Director of Studies Mathematics



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.

Journal Article Type Article
Publication Date Feb 1, 2017
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
APA6 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. doi:10.1007/s00440-015-0682-0
DOI https://doi.org/10.1007/s00440-015-0682-0
Keywords Metastability; Ising model; Random graphs; Pathwise approach
Publisher URL https://link.springer.com/article/10.1007/s00440-015-0682-0
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