Journal of Statistical Physics, Vol. 33, No. 1, 1983. p. 91-98.
We investigate the conjecture that in Ising ferromagnets, single-site magnetization (Sigma x) is a jointly concave function of the magnetic field variables. We present partial results favoring the conjecture, including a numerical survey, although we do not prove it in full generality. We also point out some implications of concavity.