Correlation inequalities for statistical models of lattice gas
We consider models of statistical mechanics of the type of lattice gas with attractive interaction of general kind. We propose a method for obtaining inequalities that connect multipoint correlation functions of different order. This method allows one, on the one hand, to strengthen similar inequali...
Saved in:
| Date: | 1998 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
|
| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4886 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511067709374464 |
|---|---|
| author | Virchenko, Yu. P. Вирченко, Ю. П. Вирченко, Ю. П. |
| author_facet | Virchenko, Yu. P. Вирченко, Ю. П. Вирченко, Ю. П. |
| author_sort | Virchenko, Yu. P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:16:32Z |
| description | We consider models of statistical mechanics of the type of lattice gas with attractive interaction of general kind. We propose a method for obtaining inequalities that connect multipoint correlation functions of different order. This method allows one, on the one hand, to strengthen similar inequalities, which can be obtained within the framework of the FKG method, and on the other hand, to obtain new inequalities. We introduce the notion of duality for models of lattice gas. We show that if, under the transformation p ⇒ 1 - p, the correlation inequalities for a model with attraction turn into the corresponding inequalities that are also satisfied, then the correlation functions of the dual model also satisfy the latter inequalities. |
| first_indexed | 2026-03-24T03:07:00Z |
| format | Article |
| fulltext |
0021
0022
0023
0024
0025
0026
0027
0028
0029
|
| id | umjimathkievua-article-4886 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:07:00Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5d/5b14e21c8c6a33ce67707d1fd1e6195d.pdf |
| spelling | umjimathkievua-article-48862020-03-18T21:16:32Z Correlation inequalities for statistical models of lattice gas Корреляционные неравенства для статистических моделей решеточного газа Virchenko, Yu. P. Вирченко, Ю. П. Вирченко, Ю. П. We consider models of statistical mechanics of the type of lattice gas with attractive interaction of general kind. We propose a method for obtaining inequalities that connect multipoint correlation functions of different order. This method allows one, on the one hand, to strengthen similar inequalities, which can be obtained within the framework of the FKG method, and on the other hand, to obtain new inequalities. We introduce the notion of duality for models of lattice gas. We show that if, under the transformation p ⇒ 1 - p, the correlation inequalities for a model with attraction turn into the corresponding inequalities that are also satisfied, then the correlation functions of the dual model also satisfy the latter inequalities. Розглядаються моделі статистичної механіки типу ґраткового газу із взаємодією притягання загального типу. Запропоновано метод одержання нерівностей, що пов'язують багатогочкові кореляційні функції різних порядків. Цей метод дозволяє, з одного боку, посилити аналої ічні нерівності, які можуть бути отримані у рамках методу FKG, а з іншого — одержати нові нерівності. Вводиться поняття дуальності для моделей ґраткового газу. Показано, що коли кореляційні нерівності для моделі з притяганням при перетворенні $p ⇒ 1 - p$ переходять у відповідні нерівності, які також виконуються, то останнім підкоряються і кореляційні функції дуальної моделі. Institute of Mathematics, NAS of Ukraine 1998-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4886 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 6 (1998); 765–773 Український математичний журнал; Том 50 № 6 (1998); 765–773 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4886/6471 https://umj.imath.kiev.ua/index.php/umj/article/view/4886/6472 Copyright (c) 1998 Virchenko Yu. P. |
| spellingShingle | Virchenko, Yu. P. Вирченко, Ю. П. Вирченко, Ю. П. Correlation inequalities for statistical models of lattice gas |
| title | Correlation inequalities for statistical models of lattice gas |
| title_alt | Корреляционные неравенства для статистических моделей решеточного газа |
| title_full | Correlation inequalities for statistical models of lattice gas |
| title_fullStr | Correlation inequalities for statistical models of lattice gas |
| title_full_unstemmed | Correlation inequalities for statistical models of lattice gas |
| title_short | Correlation inequalities for statistical models of lattice gas |
| title_sort | correlation inequalities for statistical models of lattice gas |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4886 |
| work_keys_str_mv | AT virchenkoyup correlationinequalitiesforstatisticalmodelsoflatticegas AT virčenkoûp correlationinequalitiesforstatisticalmodelsoflatticegas AT virčenkoûp correlationinequalitiesforstatisticalmodelsoflatticegas AT virchenkoyup korrelâcionnyeneravenstvadlâstatističeskihmodelejrešetočnogogaza AT virčenkoûp korrelâcionnyeneravenstvadlâstatističeskihmodelejrešetočnogogaza AT virčenkoûp korrelâcionnyeneravenstvadlâstatističeskihmodelejrešetočnogogaza |