On phase separation points for one-dimensional models
In the paper, the one-dimensional model with nearest-neighbor interactions In, n ∈ Z, and the s pin values ±1 is considered. It is known that, under some conditions on parameters of In, a phase transition occurs for this model. We define the notion of a phase separation point between two phases. We...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Allerton Press, Inc.
2009
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/1640/ http://irep.iium.edu.my/1640/1/SibAM09%5B1%5D.pdf |
| _version_ | 1848775890247352320 |
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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 | In the paper, the one-dimensional model with nearest-neighbor interactions In, n ∈ Z, and the s pin values ±1 is considered. It is known that, under some conditions on parameters of In, a phase transition occurs for this model. We define the notion of a phase separation point between two phases. We prove that the expectation value of this point is zero and its mean-square fluctuation is bounded by a constant C(β) which tends to 1/4 as β → ∞ where β = 1/T and T is the temperature. |
| first_indexed | 2025-11-14T14:21:23Z |
| format | Article |
| id | iium-1640 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:23Z |
| publishDate | 2009 |
| publisher | Allerton Press, Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16402011-12-08T01:07:06Z http://irep.iium.edu.my/1640/ On phase separation points for one-dimensional models Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich QA Mathematics In the paper, the one-dimensional model with nearest-neighbor interactions In, n ∈ Z, and the s pin values ±1 is considered. It is known that, under some conditions on parameters of In, a phase transition occurs for this model. We define the notion of a phase separation point between two phases. We prove that the expectation value of this point is zero and its mean-square fluctuation is bounded by a constant C(β) which tends to 1/4 as β → ∞ where β = 1/T and T is the temperature. Allerton Press, Inc. 2009 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1640/1/SibAM09%5B1%5D.pdf Ganikhodjaev, Nasir and Rozikov, Utkir Abdulloevich (2009) On phase separation points for one-dimensional models. Siberian Advances in Mathematics, 19 (2). pp. 75-84. ISSN 1055-1344 (P), 1934-8126 (O) http://www.springerlink.com/content/t17w380855606217/ 10.3103/S1055134409020011 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Rozikov, Utkir Abdulloevich On phase separation points for one-dimensional models |
| title | On phase separation points for one-dimensional models |
| title_full | On phase separation points for one-dimensional models |
| title_fullStr | On phase separation points for one-dimensional models |
| title_full_unstemmed | On phase separation points for one-dimensional models |
| title_short | On phase separation points for one-dimensional models |
| title_sort | on phase separation points for one-dimensional models |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1640/ http://irep.iium.edu.my/1640/ http://irep.iium.edu.my/1640/ http://irep.iium.edu.my/1640/1/SibAM09%5B1%5D.pdf |