Pirogov-Sinai theory with new contours for symmetric models

Pirogov-Sinai theory with new contours for symmetric models

The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very general and rather difficult. Intuitively clear that the Peierls a...

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Main Authors: Ganikhodjaev, Nasir, Rozikov, Utkir Abdulloevich
Format: Article
Language:English
Published: World Scientific Publishing Co. 2008
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/1644/
http://irep.iium.edu.my/1644/
http://irep.iium.edu.my/1644/
http://irep.iium.edu.my/1644/1/Pirogov_Sinai%2C2008%2C537.zip
id iium-1644
recordtype eprints
spelling iium-16442011-11-24T07:23:31Z http://irep.iium.edu.my/1644/ Pirogov-Sinai theory with new contours for symmetric models Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich QA Mathematics The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very general and rather difficult. Intuitively clear that the Peierls argument does work for any symmetric model. But contours defined in Pirogov–Sinai theory do not work if one wants to use Peierls argument for more general symmetric models. We give a new definition of contour which allows relatively easier proof to the main result of the Pirogov–Sinai theory for symmetric models. Namely, our contours allow us to apply the classical Peierls argument (with contour removal operation). World Scientific Publishing Co. 2008-06 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1644/1/Pirogov_Sinai%2C2008%2C537.zip Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2008) Pirogov-Sinai theory with new contours for symmetric models. International Journal of Geometric Methods in Modern Physics, 5 (4). pp. 537-546. ISSN 0219-8878 (P), 1793-6977 (O) http://www.worldscinet.com/ijgmmp/05/0504/S0219887808002928.html 10.1142/S0219887808002928
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodjaev, Nasir
Rozikov, Utkir Abdulloevich
Pirogov-Sinai theory with new contours for symmetric models
description The contour argument was introduced by Peierls for two dimensional Ising model. Peierls benefited from the particular symmetries of the Ising model. For non-symmetric models the argument was developed by Pirogov and Sinai. It is very general and rather difficult. Intuitively clear that the Peierls argument does work for any symmetric model. But contours defined in Pirogov–Sinai theory do not work if one wants to use Peierls argument for more general symmetric models. We give a new definition of contour which allows relatively easier proof to the main result of the Pirogov–Sinai theory for symmetric models. Namely, our contours allow us to apply the classical Peierls argument (with contour removal operation).
format Article
author Ganikhodjaev, Nasir
Rozikov, Utkir Abdulloevich
author_facet Ganikhodjaev, Nasir
Rozikov, Utkir Abdulloevich
author_sort Ganikhodjaev, Nasir
title Pirogov-Sinai theory with new contours for symmetric models
title_short Pirogov-Sinai theory with new contours for symmetric models
title_full Pirogov-Sinai theory with new contours for symmetric models
title_fullStr Pirogov-Sinai theory with new contours for symmetric models
title_full_unstemmed Pirogov-Sinai theory with new contours for symmetric models
title_sort pirogov-sinai theory with new contours for symmetric models
publisher World Scientific Publishing Co.
publishDate 2008
url http://irep.iium.edu.my/1644/
http://irep.iium.edu.my/1644/
http://irep.iium.edu.my/1644/
http://irep.iium.edu.my/1644/1/Pirogov_Sinai%2C2008%2C537.zip
first_indexed 2023-09-18T20:09:04Z
last_indexed 2023-09-18T20:09:04Z
_version_ 1777407355187625984

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