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Phys. Rev. B 42, 10360–10380 (1990)

Exact theories of m-component quadrupolar systems showing a first-order phase transition

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Kaoru Ohno
Department of Physics, College of General Education, Tohoku University, Kawauchi, Sendai, Miyagi 980, Japan

Hans-Otto Carmesin
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
Department of Chemistry, State University of New York, Albany, New York 12222

Hikaru Kawamura
Department of Physics, College of General Education, Osaka University, Toyonaka, Osaka 560, Japan

Yutaka Okabe
Department of Physics, Faculty of Science, Tohoku University, Aoba, Sendai, Miyagi 980, Japan

Received 27 August 1990; published in the issue dated 1 December 1990

Several statistical-thermodynamic theories involving an exact solution in one dimension (d=1), high- and low-temperature series expansions, and an exact solution of an infinite-range system (mean-field theory) are presented for a quadrupolar spin model whose Hamiltonian is described with m-component classical spins Si as scrH=-1/2 tsumi,j=1N Jij(Si⋅Sj)2 on a d-dimensional lattice. An orientational phase transition is analyzed systematically as a function of m. The transition is first order generally for 2<m≤∞ and d>2. We evaluate the transition point and the discontinuity in energy as a function of m. We also present exact solutions in the m→∞ limit for arbitrary spatial dimensions.

© 1990 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevB.42.10360
DOI:
10.1103/PhysRevB.42.10360
PACS:
64.60.Cn, 64.70.Md
 
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