Partition function zeros of the antiferromagnetic spin- 1 2 Ising-Heisenberg model on a diamond chain

N.S. Ananikian, V.V. Hovhannisyan, Ralph Kenna

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    Abstract

    The partition function zeros of the antiferromagnetic spin-1/2 Ising–Heisenberg model on a diamond chain are studied using the transfer matrix method. Analytical equations for the distributions of Yang–Lee and Fisher zeros are derived. The Yang–Lee zeros are located on an arc of the unit circle and on the negative real axis in the complex magnetic-fugacity plane. In the limit T→0T→0 the distribution pinches the positive real axis, precipitating a phase transition. Fisher zeros manifest more complicated distributions, depending on the values of the exchange parameters and external field. Densities of both categories of zeros are also studied. The distributions of Fisher zeros are investigated for different values of model parameters. The Yang–Lee and Fisher edge singularity exponents are shown to be identical. They are universal in nature and are calculated to be σ=−1/2.
    Original languageEnglish
    Pages (from-to)51-60
    JournalPhysica A: Statistical Mechanics and its Applications
    Volume396
    Early online date19 Nov 2013
    DOIs
    Publication statusPublished - 2014

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    Keywords

    • Ising–Heisenberg model
    • diamond chain
    • Yang–Lee zeros
    • Fisher zeros
    • superstability

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