Selfconsistent singularities of the static correlation function at the critical point

The Behaviour of Thermodynamic Quantities Close to the Critical Point. The Itinerant Ferromagnet

“…In the equation for S, on the other hand, each term contains two 6, one of each spin value. It is this fact, coupled with the coincidence of the singularities, that produces a logarithmic singularity in the static correlation function, as we have shown in [7].…”

“…The following integral equations for fi and S are obtained in exactly the same manner as (2.8) and (2.9) of [7], and are based on (3.4) and (3.5) of [lo]. They are written to order 5 and exhibit an explicit dependence on 6;""".…”

“…As shown in ch. 4 of [7], we can use the following approxiniate form in the energy denominators, where e,,k=ke in the absence of an external magnetic field and a is a constant of appropriate dimensionality: where the spontaneous magnetization m(.) goes to zero at T = T,.…”

“…We will continue here the analysis contained in our earlier paper [7], where the static correlation function was examined at the critical temperature. The idea there, as in the present work, is to generalize the molecular field view in which the collective forces generate a molecular field which eventually, at the phase transition, yields divergences of certain quantities.…”

“…It is reproduced here because it will be needed for developing the later chapters. The discussion in [7] was restricted to the behaviour of the static correlation function at T=T,, where T, denotes the criitical temperature, and a logarithmic deviation from the Ornstein-Zernike behaviour was found. In the present work, we consider the correlation function and the spontaneous magnetization at a temperature T close to, but not equal to, T,.…”