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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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World Scientific Publishing Co.
2008
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| Online Access: | http://irep.iium.edu.my/1644/ http://irep.iium.edu.my/1644/1/Pirogov_Sinai%2C2008%2C537.zip |
| _version_ | 1848775891293831168 |
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| author | Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_facet | Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| 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). |
| first_indexed | 2025-11-14T14:21:24Z |
| format | Article |
| id | iium-1644 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:24Z |
| publishDate | 2008 |
| publisher | World Scientific Publishing Co. |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich Pirogov-Sinai theory with new contours for symmetric models |
| title | 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_short | Pirogov-Sinai theory with new contours for symmetric models |
| title_sort | pirogov-sinai theory with new contours for symmetric models |
| topic | QA Mathematics |
| 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 |