Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula
We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco form...
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| Format: | Journal article |
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1996
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| _version_ | 1826269711929704448 |
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| author | Szabo, R Wheater, J |
| author_facet | Szabo, R Wheater, J |
| author_sort | Szabo, R |
| collection | OXFORD |
| description | We study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of the large-N character expansion approach as well as potential physical applications of our results. |
| first_indexed | 2024-03-06T21:29:23Z |
| format | Journal article |
| id | oxford-uuid:44263110-e0df-484e-a448-aff68fb5e2ab |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:29:23Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | oxford-uuid:44263110-e0df-484e-a448-aff68fb5e2ab2022-03-26T14:59:49ZCurvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco FormulaJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:44263110-e0df-484e-a448-aff68fb5e2abSymplectic Elements at Oxford1996Szabo, RWheater, JWe study the large-N limit of a class of matrix models for dually weighted triangulated random surfaces using character expansion techniques. We show that for various choices of the weights of vertices of the dynamical triangulation the model can be solved by resumming the Itzykson-Di Francesco formula over congruence classes of Young tableau weights modulo three. From this we show that the large-N limit implies a non-trivial correspondence with models of random surfaces weighted with only even coordination number vertices. We examine the critical behaviour and evaluation of observables and discuss their interrelationships in all models. We obtain explicit solutions of the model for simple choices of vertex weightings and use them to show how the matrix model reproduces features of the random surface sum. We also discuss some general properties of the large-N character expansion approach as well as potential physical applications of our results. |
| spellingShingle | Szabo, R Wheater, J Curvature Matrix Models for Dynamical Triangulations and the Itzykson-DiFrancesco Formula |
| title | Curvature Matrix Models for Dynamical Triangulations and the
Itzykson-DiFrancesco Formula |
| title_full | Curvature Matrix Models for Dynamical Triangulations and the
Itzykson-DiFrancesco Formula |
| title_fullStr | Curvature Matrix Models for Dynamical Triangulations and the
Itzykson-DiFrancesco Formula |
| title_full_unstemmed | Curvature Matrix Models for Dynamical Triangulations and the
Itzykson-DiFrancesco Formula |
| title_short | Curvature Matrix Models for Dynamical Triangulations and the
Itzykson-DiFrancesco Formula |
| title_sort | curvature matrix models for dynamical triangulations and the itzykson difrancesco formula |
| work_keys_str_mv | AT szabor curvaturematrixmodelsfordynamicaltriangulationsandtheitzyksondifrancescoformula AT wheaterj curvaturematrixmodelsfordynamicaltriangulationsandtheitzyksondifrancescoformula |