Magnetization of Ising model in nonzero magnetic field

Knowing only the zero-field magnetization (e.g., Yang's result) of the Ising model in any number of dimensions, one can construct a lower bound on m(h), the magnetization in finite field. Knowledge of u, the internal energy per bond, enables a more efficient lower bound to be constructed. Both are applications of the Griffiths inequality, as recently generalized by Kelly and Sherman, and should prove useful in the lattice gas problem where it is essential to know m(h).