DOI: 10.1214/105051605000000421. Analysis of phase transitions in the mean-field Blume–Emery

Analysis of phase transitions in the mean-field Blume–Emery–Griffiths model

10.1214/105051605000000421

Crossref journal-article

Institute of Mathematical Statistics

The Annals of Applied Probability (108)

Bibliography

Ellis, R. S., Otto, P. T., & Touchette, H. (2005). Analysis of phase transitions in the mean-field BlumeâEmeryâGriffiths model. The Annals of Applied Probability, 15(3).

Authors 3

Richard S. Ellis (first)
Peter T. Otto (additional)
Hugo Touchette (additional)

References 25 Referenced 34

Dates

Type	When
Created	20 years, 1 month ago (July 15, 2005, 10 a.m.)
Deposited	4 years, 3 months ago (May 6, 2021, 6:43 p.m.)
Indexed	5 months, 1 week ago (March 19, 2025, 11:27 a.m.)
Issued	20 years ago (Aug. 1, 2005)
Published	20 years ago (Aug. 1, 2005)
Published Print	20 years ago (Aug. 1, 2005)

Funders 0

None

BibTeX

@article{Ellis_2005, title={Analysis of phase transitions in the mean-field Blume–Emery–Griffiths model}, volume={15}, ISSN={1050-5164}, url={http://dx.doi.org/10.1214/105051605000000421}, DOI={10.1214/105051605000000421}, number={3}, journal={The Annals of Applied Probability}, publisher={Institute of Mathematical Statistics}, author={Ellis, Richard S. and Otto, Peter T. and Touchette, Hugo}, year={2005}, month=aug }

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      "DOI": "10.1103/PhysRevA.4.1071"
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