Local magnetic field distributions: Two-dimensional Ising models

We show that the statistical mechanics of Ising models can be conveniently reformulated in terms of the local magnetic field probability distribution function P(h). It is shown that for arbitrary exchange interactions Jij, which may or may not be random, both thermodynamic quantities such as magnetization, specific heat, etc., and the neutron scattering law S(k,) can be obtained from P(h). Indeed S(k,) provides a direct measurement of the symmetric part of P(h) which also determines the energy, specific heat, etc., while the magnetization can be obtained from the antisymmetric part of P(h). As an example, specific results for P(h) are presented for the honeycomb, square, and triangular lattices with constant nearest-neighbor interactions. All three lattices exhibit a pronounced dip in the center of P(h) at the transition temperature.