Absence of an intermediate phase for a general class of one-component ferromagnetic models

For a general class of ferromagnetic models of one-component spins it is rigorously shown that (i) the phase transition, at zero magnetic field, occurs directly from the high-temperature phase to the low-temperature regime; (ii) the critical exponent is bounded by its mean-field value, 1/2; (iii) the critical temperature can be rigorously estimated to any desired accuracy, by finite-size calculations; and (iv) Tc depends continuously on the model in domains over which the models satisfy uniformly a new regularity condition.