Local magnetic field distributions. II. Further results

The concept and character of the local magnetic field distribution P(h), developed in an earlier paper, is extended to higher space and spin dimensions and to several special but spatially periodic systems, disorder being the subject of a future paper. For Ising spins on standard lattices, P(h) is shown to have a shape which is dimension dependent but relatively coordination independent. While in two dimensions (2D) P(h) has a dip at h=0 at $T_c$, in 3D it is extremely flat near the origin, in 4D it is pseudo-Gaussian, while in all dimensions it is qualitatively similar to a discrete form of the corresponding universal block-spin probability function. Bethe lattices, studied for all spin dimensions, are shown to be quite different. Results are also presented for P(h) and the ground-state degeneracies of some one-dimensional frustrated systems exhibiting high-degeneracy disorder points.