First-order transitions, symmetry, and the element of-expansion

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The group theoretical method of Landau and Lifshitz was used to derive effective Hamiltonians for certain paramagnetic to antiferromagnetic transitions having order-parameters with n greater than or equal to 4 components. A renormalization group analysis in 4-epsilon dimensions was performed. The first- order nature of the order-disorder transitions in Cr(n = 12), Eu(n = 12), UO$sub 2$(n = 6), and MnO(n = 8) can be explained by noting that the corresponding Hamiltonians possess no stable fixed points in 4-epsilon dimensions. It is predicted that all fcc type I(anti m perpendicular anti k), type II and type III(anti m perpendicular [100], ... continued below

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Pages: 37

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Mukamel, D.; Krinsky, S. & Bak, P. January 1, 1975.

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The group theoretical method of Landau and Lifshitz was used to derive effective Hamiltonians for certain paramagnetic to antiferromagnetic transitions having order-parameters with n greater than or equal to 4 components. A renormalization group analysis in 4-epsilon dimensions was performed. The first- order nature of the order-disorder transitions in Cr(n = 12), Eu(n = 12), UO$sub 2$(n = 6), and MnO(n = 8) can be explained by noting that the corresponding Hamiltonians possess no stable fixed points in 4-epsilon dimensions. It is predicted that all fcc type I(anti m perpendicular anti k), type II and type III(anti m perpendicular [100], anti k = [1/2 01]) antiferromagnetic transitions are first-order. The work is intended to serve as a guide in an experimental search for new examples of first-order transitions. A 2m-component Hamiltonian is also considered which possesses a unique, nonisotropic, stable fixed point for each value of 2m greater than or equal to 4. When 2m = 4, the Hamiltonian describes the paramagnetic to antiferromagnetic transitions in TbAu$sub 2$, DyC$sub 2$, Tb, Ho, Dy, and the structural transition in NbO$sub 2$. If these transitions are second-order, it is predicted they all belong to the same universality class. For 2m = 6, the Hamiltonian describes the antiferromagnetic transitions in TbD$sub 2$, Nd, K$sub 2$IrCl$sub 6$, and MnS$sub 2$. These transitions belong to a single universality class. (auth)

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Pages: 37

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  • 21. annual conference on magnetism and magnetic materials, Philadelphia, Pennsylvania, USA, 9 Dec 1975

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  • Report No.: BNL--20619
  • Report No.: CONF-751209--16
  • Grant Number: None
  • Office of Scientific & Technical Information Report Number: 4060578
  • Archival Resource Key: ark:/67531/metadc870251

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  • January 1, 1975

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  • Sept. 16, 2016, 12:32 a.m.

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  • Sept. 21, 2016, 7:01 p.m.

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Mukamel, D.; Krinsky, S. & Bak, P. First-order transitions, symmetry, and the element of-expansion, article, January 1, 1975; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc870251/: accessed September 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.