Abstract
Elementary proofs of the first and second Griffiths-Kelly-Sherman (GKS) inequalities are given for higher-spin Ising systems with a Hamiltonian containing only a quadratic form in the spin variables and integer powers of single spin variables. These proofs are obtained using Gaussian random variables. A slight generalization of previous results has been obtained in that the coefficients of the even powers of the spin variables are allowed to be negative.
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References
R. B. Griffiths, inPhase Transitions and Critical Phenomena, Vol. I, C. Domb and M. S. Green (eds.), Academic Press, New York (1972), and references given there.
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Work supported by NSF Grant GP-36564X.
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Monroe, J.L., Siegert, A.J.F. GKS inequalities for arbitrary spin ising ferromagnets. J Stat Phys 10, 237–244 (1974). https://doi.org/10.1007/BF01016178
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DOI: https://doi.org/10.1007/BF01016178