The Critical Exponents of Crystalline Random Surfaces
We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The co...
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| Format: | Journal article |
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1995
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| _version_ | 1826297766337314816 |
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| author | Wheater, J |
| author_facet | Wheater, J |
| author_sort | Wheater, J |
| collection | OXFORD |
| description | We report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be $\nu=0.71(5)$ from the tangent-tangent correlation function whereas we find $\nu=0.73(6)$ by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent $\alpha=0.58(10)$; this is a good fit to the specific heat on a $64^2$ lattice with a $\chi^2$ per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of $\alpha$. Our measurements of the normal-normal correlation functions suggest that the model in the crumpled phase is described by an effective field theory which deviates from a free field theory only by super-renormalizable interactions. |
| first_indexed | 2024-03-07T04:36:40Z |
| format | Journal article |
| id | oxford-uuid:d028dcbb-988a-47d8-89ee-f6f0dfa305eb |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:36:40Z |
| publishDate | 1995 |
| record_format | dspace |
| spelling | oxford-uuid:d028dcbb-988a-47d8-89ee-f6f0dfa305eb2022-03-27T07:47:59ZThe Critical Exponents of Crystalline Random SurfacesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d028dcbb-988a-47d8-89ee-f6f0dfa305ebSymplectic Elements at Oxford1995Wheater, JWe report on a high statistics numerical study of the crystalline random surface model with extrinsic curvature on lattices of up to $64^2$ points. The critical exponents at the crumpling transition are determined by a number of methods all of which are shown to agree within estimated errors. The correlation length exponent is found to be $\nu=0.71(5)$ from the tangent-tangent correlation function whereas we find $\nu=0.73(6)$ by assuming finite size scaling of the specific heat peak and hyperscaling. These results imply a specific heat exponent $\alpha=0.58(10)$; this is a good fit to the specific heat on a $64^2$ lattice with a $\chi^2$ per degree of freedom of 1.7 although the best direct fit to the specific heat data yields a much lower value of $\alpha$. Our measurements of the normal-normal correlation functions suggest that the model in the crumpled phase is described by an effective field theory which deviates from a free field theory only by super-renormalizable interactions. |
| spellingShingle | Wheater, J The Critical Exponents of Crystalline Random Surfaces |
| title | The Critical Exponents of Crystalline Random Surfaces |
| title_full | The Critical Exponents of Crystalline Random Surfaces |
| title_fullStr | The Critical Exponents of Crystalline Random Surfaces |
| title_full_unstemmed | The Critical Exponents of Crystalline Random Surfaces |
| title_short | The Critical Exponents of Crystalline Random Surfaces |
| title_sort | critical exponents of crystalline random surfaces |
| work_keys_str_mv | AT wheaterj thecriticalexponentsofcrystallinerandomsurfaces AT wheaterj criticalexponentsofcrystallinerandomsurfaces |