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- W1982492155 abstract "The Lee‐Yang theorem for the zeros of the partition function of a ferromagnetic Ising model with real pair spin interactions is extended to general Ising models with complex many‐spin interactions (satisfying appropriate ``ferromagnetic'' and spin inversion symmetry conditions). When many‐spin interactions are present, all zeros lie on the imaginary Hz‐axis for sufficiently low (but fixed) T, but, in general, some leave the imaginary axis as T → ∞. The extended Ising theorem is used to prove the same result for a Heisenberg system of arbitrary spin with the real anisotropic pair interaction Hamiltonian Hij=−(JijzSizSjz+JijxSixSjx+JijySiySjy) in an arbitrary transverse field (Hx, Hy) under the ``ferromagnetic'' condition Jijz≥|Jijx| and Jijz≥|Jijy|. The analyticity of the limiting free energy of such a Heisenberg ferromagnet and the absence of a phase transition are thereby established for all (real) nonzero magnetic fields Hz. The Ising theorem is also applied to hydrogen‐bonded ferroelectric models to prove, in particular, that the zeros for the KDP model lie on the imaginary electric field axis for all T below the transition temperature Tc." @default.
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- W1982492155 date "1971-02-01" @default.
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- W1982492155 title "Zeros of the Partition Function for the Heisenberg, Ferroelectric, and General Ising Models" @default.
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- W1982492155 doi "https://doi.org/10.1063/1.1665583" @default.
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