ABSTRACT
For the moment, let us assume that = Γ , independent
of k. We can write (11. 37) in terms of σ(χ, t):
= -Γ 2(a2a - c v 2o) + ζ ,
(11.38)
( ζ (x, t) ζ ( x 7, t ' ) ) = 2Γ δ (x — x 7 ) δ (t - t 7 ) .
As before, it is understood that σ(χ, t) contains only
Fourier components with k < A. Equation (11.38) exp lic it-
ly describes the dynamics over a region of size A * . It is
a 1'loca l11 equation of motion, in the same spirit as model
(5) discussed in Chapter II. It should be kept in mind that
our purpose here is to derive cr it ica l dynamics, which con-
cerns large-sca le behaviors, from local equations of
motion, which are based on dynamics over a much sm aller
scale. The phenomenological constant Γ and the random
field ζ are supposed to simulate the effect of dynamical
processes over a scale A ^ . Therefore, Γ is expected
to be a smooth function of temperature and can be con-
sidered to be a constant within a small temperature range
near T^ . This is the same argument as that in Chapter II
leading to the conclusion that parameters in the block
Hamiltonian are smooth functions of T.
