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

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

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    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

    Fingerprint

    Heisenberg Model
    Strombus or kite or diamond
    Partition Function
    Ising Model
    partitions
    diamonds
    Zero
    matrix methods
    Edge Singularity
    Transfer Matrix Method
    arcs
    exponents
    Unit circle
    External Field
    Arc of a curve
    Phase Transition
    Exponent
    Model

    Bibliographical note

    The full text of this item is not available from the repository.

    Keywords

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

    Cite this

    Partition function zeros of the antiferromagnetic spin- 1 2 Ising-Heisenberg model on a diamond chain. / Ananikian, N.S.; Hovhannisyan, V.V.; Kenna, Ralph.

    In: Physica A: Statistical Mechanics and its Applications, Vol. 396, 2014, p. 51-60.

    Research output: Contribution to journalArticle

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    AU - Kenna, Ralph

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    AB - 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.

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