Rigorous results for Ising ferromagnets of general spin with degeneracy or symmetric potentials

Publisher Website
Google Scholar
Abstract
The circle theorem of Lee and Yang is proved for Ising ferromagnets of general spin with degeneracy or symmetric potentials φj(−Sj) = φj(Sj); i.e., all the zeros of the partition function Ξ = Tr exp (ΣKijSiSj + βλΣjφj(Sj) + hΣjSj) lie on the unit circle of the complex fugacity plane (z = e−h) for Kij ≥ 0, λ ≥ 0, and for ``nondecreasing functions'' φj(Sj); φj(S) ≥ φj(S − 1) ≥ … ≥ φj(1/2) [or φj(0)], including the proof by Griffiths for the usual Ising model of arbitrary spin. The analyticity of the limiting free energy of such a generalized Ising ferromagnet and the absence of a phase transition are thereby established for all (real) nonzero magnetic field. Griffiths‐Kelly‐Sherman inequalities on spin correlations and Baker's inequalities on critical exponents are discussed in connection with the above model and also in a more general case.