Ising model critical slowing down

Critical slowing down in Ising and Potts models 140... 

Potts models suffer from critical slowing down in just the same way as the Ising model. All the algorithms discussed in this chapter can be generalized to Potts models. Here we discuss the example of the Wolff algorithm, whose appropriate generalization is as follows ... 

If a material is ferroelectric, local field effects must be taken into account in order to determine the intrinsic individual relaxation time. The collective relaxation times are characterized by a critical slowing down, as observed for the reorientations of HjO and HjO in HUP or of Hse04 and in NH4HSe04 . The Ising model and molecular field approximation lead to the definition of a new relaxation time ... 

Thus oj(q = 0) vanishes as co q = 0) oc Xt % Yl" — % <2 n>> and eq. (201) hence implies the classical value Zd = 2 — ij. Although eq. (206) thus suggests a relationship between the dynamic exponent and static ones, this is not true if effects due to non-mean-field critical fluctuations are taken into account. In fact, for the kinetic Ising model (Kawasaki, 1972) extensive numerical calculations imply that z. 2.18 in d = 2 dimensions (Dammann and Reger, 1993 Stauffer, 1992 Landau et al., 1988) rather than Zc = 2 - r) = 1.75. Note also [this is already evident from eq. (206)] that not all fluctuations slow down as Tc is approached but only those associated with long wavelength order parameter variations. One can express this fact in terms of a dynamic scaling principle... 

---