{"title":"几何受挫伊辛反铁磁体的非弹性中子散射:精确解","authors":"K. A. Muttalib, J. H. Barry","doi":"10.1103/physrevb.110.024414","DOIUrl":null,"url":null,"abstract":"Employing transformations of planar Ising models (decoration-decimation followed by star-triangle), the frustrated antiferromagnetic kagomé Ising model is mapped to the known disordered region of the ferromagnetic triangular Ising model. Thereafter, with supplemental aid of mapping theorems and linear algebraic correlation identities, correlations in the frustrated kagomé Ising model are determined at all temperatures, enabling exact solutions to be obtained in the neutron scattering problem. More particularly, the scattering function <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mi>S</mi><mrow><mi>x</mi><mi>x</mi></mrow></msup><mrow><mo>(</mo><mover accent=\"true\"><mi>q</mi><mo>⃗</mo></mover><mo>,</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math> is uniform in momentum <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mover accent=\"true\"><mi>q</mi><mo>⃗</mo></mover></math> and exhibits Dirac <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>δ</mi></math> functions at select scattering frequencies, where each select frequency is associated with a temperature-dependent scattering amplitude. The scattering solutions are compared with those of the ferromagnetic kagomé Ising model.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inelastic neutron scattering from a geometrically frustrated Ising antiferromagnet: Exact solutions\",\"authors\":\"K. A. Muttalib, J. H. Barry\",\"doi\":\"10.1103/physrevb.110.024414\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Employing transformations of planar Ising models (decoration-decimation followed by star-triangle), the frustrated antiferromagnetic kagomé Ising model is mapped to the known disordered region of the ferromagnetic triangular Ising model. Thereafter, with supplemental aid of mapping theorems and linear algebraic correlation identities, correlations in the frustrated kagomé Ising model are determined at all temperatures, enabling exact solutions to be obtained in the neutron scattering problem. More particularly, the scattering function <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mrow><msup><mi>S</mi><mrow><mi>x</mi><mi>x</mi></mrow></msup><mrow><mo>(</mo><mover accent=\\\"true\\\"><mi>q</mi><mo>⃗</mo></mover><mo>,</mo><mi>ω</mi><mo>)</mo></mrow></mrow></math> is uniform in momentum <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mover accent=\\\"true\\\"><mi>q</mi><mo>⃗</mo></mover></math> and exhibits Dirac <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><mi>δ</mi></math> functions at select scattering frequencies, where each select frequency is associated with a temperature-dependent scattering amplitude. The scattering solutions are compared with those of the ferromagnetic kagomé Ising model.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.024414\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.024414","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Inelastic neutron scattering from a geometrically frustrated Ising antiferromagnet: Exact solutions
Employing transformations of planar Ising models (decoration-decimation followed by star-triangle), the frustrated antiferromagnetic kagomé Ising model is mapped to the known disordered region of the ferromagnetic triangular Ising model. Thereafter, with supplemental aid of mapping theorems and linear algebraic correlation identities, correlations in the frustrated kagomé Ising model are determined at all temperatures, enabling exact solutions to be obtained in the neutron scattering problem. More particularly, the scattering function is uniform in momentum and exhibits Dirac functions at select scattering frequencies, where each select frequency is associated with a temperature-dependent scattering amplitude. The scattering solutions are compared with those of the ferromagnetic kagomé Ising model.
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