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Partial ordering at the ground state of frustrated spin-S Ising models

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  • Lipowski, Adam
  • Horiguchi, Tsuyoshi
  • Honda, Yasushi

Abstract

We show that a partial ordering appears in the limit S → ∞ at the ground state of the 1D spin-S antiferromagnetic Ising model with next-nearest-neighbour interaction. This is an analogue of the ordering which appears at finite S = Sc ≈ 3 in the nearest-neighbour Ising antiferromagnet on the triangular lattice. We also show that the ground-state problems.in these spin-S models can be mapped into reweighted S = 12 ground-state problems. Thus the emergence of the order for the model on the triangular lattice is related to the roughening transition in a certain SOS model. For the model on the triangular lattice, the transfer-matrix method is used to calculate the critical exponent η and the central charge c. For 12 ⩽S⩽2, the central charge is almost constant and very close to unity. However, in the rough phase for 2 < S < Sc the central charge slightly deviates from unity, which is in contradiction with some predictions based on the conformal invariance. Explanation of such a deviation which relates the ground-state problem with a certain long-range interacting hard hexagon model is also proposed.

Suggested Citation

  • Lipowski, Adam & Horiguchi, Tsuyoshi & Honda, Yasushi, 1997. "Partial ordering at the ground state of frustrated spin-S Ising models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 237(1), pages 297-319.
    • Handle: RePEc:eee:phsmap:v:237:y:1997:i:1:p:297-319
    DOI: 10.1016/S0378-4371(96)00428-1
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    References listed on IDEAS

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    1. Fukui, Yoshihiko & Horiguchi, Tsuyoshi, 1993. "Ground state properties of chiral XY-model on a one-dimensional lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(3), pages 580-598.
    2. Horiguchi, Tsuyoshi, 1995. "Decomposition of Ising spin of spin-S Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 214(3), pages 452-460.
    3. Urban, Francis & Nightingale, Ray, 1993. "World Population by Country and Region, 1950-90 and Projections to 2050," Staff Reports 278691, United States Department of Agriculture, Economic Research Service.
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