Color Representations of Ising Models

Malin P. Forsström ()
Additional contact information
Malin P. Forsström: KTH Royal Institute of Technology

Journal of Theoretical Probability, 2022, vol. 35, issue 1, 603-635

Abstract: Abstract In Steif and Tykesson (J Prob 16:899–955, 2019), the authors introduced the so-called general divide and color models. One of the best-known examples of such a model is the Ising model with external field $$ h = 0 $$ h = 0 , which has a color representation given by the random cluster model. In this paper, we give necessary and sufficient conditions for this color representation to be unique. We also show that if one considers the Ising model on a complete graph, then for many $$ h > 0 $$ h > 0 , there is no color representation. This shows, in particular, that any generalization of the random cluster model which provides color representations of Ising models with external fields cannot, in general, be a generalized divide and color model. Furthermore, we show that there can be at most finitely many $$ \beta > 0 $$ β > 0 at which the random cluster model can be continuously extended to a color representation for $$ h \not = 0 $$ h ≠ 0 .

Keywords: 60G99; 60K35 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-020-01051-8 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01051-8

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-020-01051-8

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().