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On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. I

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  • Siskens, Th.J.
  • Capel, H.W.
  • Gaemers, K.J.F.

Abstract

The one-dimensional anisotropic XY model with antisymmetric nearest-neighbour interactions (Dzyaloshinsky interactions) in the presence of a magnetic field B in the z direction is investigated. Special attention is given to the critical behaviour of the system. In the ground state, the susceptibility χzz has a logarithmic singularity as B → 1 provided that the strength Δ of the Dzyaloshinsky interaction obeys the inequality |Δ| ≤ |γ|, where γ is the anisotropy parameter. However, if |Δ| #62; |γ|, χzz diverges with a power -12 singularity as B ↑ (1 + Δ2 - γ2)12. The specific heat is studied for low temperatures. Furthermore for a few special values of γ and B the static correlation functions 〈SαjSβk〉 are evaluated in the low-temperature limit, for α, β = x, y, z and |j - k| = 1, 2. Finally we consider the chain with Dzyaloshinsky interactions only.

Suggested Citation

  • Siskens, Th.J. & Capel, H.W. & Gaemers, K.J.F., 1975. "On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. I," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 79(3), pages 259-295.
    • Handle: RePEc:eee:phsmap:v:79:y:1975:i:3:p:259-295
    DOI: 10.1016/0378-4371(75)90029-1
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    Cited by:

    1. Perk, J.H.H. & Capel, H.W., 1978. "Transverse correlations in the inhomogeneous one-dimensional XY-model at infinite temperature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(1), pages 163-184.
    2. Braeter, H. & Kowalski, J.M., 1977. "On the thermodynamics of the random one-dimensional Ising chain in a transverse field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(2), pages 243-257.
    3. Siskens, Th.J. & Capel, H.W., 1975. "On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. II," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 79(3), pages 296-311.

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