{"title":"Application of the spherical approximation to several specific dipolar crystals","authors":"M. Marrenga , Th. Niemeijer","doi":"10.1016/0031-8914(74)90375-9","DOIUrl":null,"url":null,"abstract":"<div><p>The spherical approximation is considered for dipole—dipole interactions. Numerical calculations of the critical temperature of two compounds, Ce<sub>2</sub>Mg<sub>3</sub>(NO<sub>3</sub>)<sub>12</sub>⋯24H<sub>2</sub>O and Dy(C<sub>2</sub>H⋯SO<sub>4</sub>)<sub>3</sub> ⋯9H<sub>2</sub>O, are presented. Good agreement with experimental data is found. The Luttinger—Tisza calculations are shown to give the exact classical ground state in these two compounds, whereas this calculation is shown to fail in Er(C<sub>2</sub>H<sub>5</sub>⋯SO<sub>4</sub>)<sub>3</sub>⋯9H<sub>2</sub>O.</p><p>It is found that in some systems the longe-range effects can be described by introducing an extra degree of freedom in the system, and the critical behaviour is therefore similar to that of a system with short-range interactions on a four-dimensional lattice.</p></div>","PeriodicalId":55605,"journal":{"name":"Physica","volume":"78 3","pages":"Pages 469-489"},"PeriodicalIF":0.0000,"publicationDate":"1974-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0031-8914(74)90375-9","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0031891474903759","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
The spherical approximation is considered for dipole—dipole interactions. Numerical calculations of the critical temperature of two compounds, Ce2Mg3(NO3)12⋯24H2O and Dy(C2H⋯SO4)3 ⋯9H2O, are presented. Good agreement with experimental data is found. The Luttinger—Tisza calculations are shown to give the exact classical ground state in these two compounds, whereas this calculation is shown to fail in Er(C2H5⋯SO4)3⋯9H2O.
It is found that in some systems the longe-range effects can be described by introducing an extra degree of freedom in the system, and the critical behaviour is therefore similar to that of a system with short-range interactions on a four-dimensional lattice.
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