Journal of Statistical Physics, Vol. 47, Nos. 3/4, 1987, p. 343-374
For a family of translation-invariant, ferromagnetic, one-component spin
systems — which includes Ising and (r 4 models — we prove that (i)the phase
transition is sharp in the sense that at zero magnetic field the high- and low-
temperature phases extend up to a common critical point, and (ii)the critical
exponent fl obeys the mean field bound fl ~< 1/2. The present derivation of these
nonperturbative statements is not restricted to "regular" systems, and is based
on a new differential inequality whose Ising model version is M <~ flh/. + M3+
tiM z OM/~fl. The significance of the inequality was recognized in a recent work
on related problems for percolation models, while the inequality itself is related
to previous results, by a number of authors, on ferromagnetic and percolation
models.