Concavity of Magnetization of an Ising Ferromagnet in a Positive External Field

Source abstract

An inequality for correlation functions in an Ising model with purely ferromagnetic interactions between pairs of spins is established and used to show that the magnetization in such a model is a concave function of external field H for H > 0. The concavity of magnetization, which holds not only for spin-½ but also for arbitrary-spin Ising ferromagnets, provides a basis for certain thermodynamic inequalities near the ferromagnetic critical point, including one involving the ``high temperature'' indices α and γ.