DESCRIPTION OF CRITICAL-DYNAMICS BY STATIC GEOMETRY OF CLUSTERS

Critical slowing-down of relaxation (exponent z) is modelled by clusters, which grow and recede at the end of connected sequences of particles, Consequently the relaxation time of a cluster of size s is proportional to the number of back and forth steps needed to travel its typical connected length l(s). This and an assumption on mutual screening of ends, lead to z = [(2.5rho - 0.25)(gamma + beta) - beta]/nu, where rho is a static geometric exponent in l(s) approximately s(rho). Ising exponents p measured (elsewhere), with the help of simulation, give z(rho,beta,nu). In addition, a Flory-like approximation is derived here; it relates rho to beta and nu analytically, giving z(beta,nu). In D = 2, 3 and 4 - epsilon, respectively, we find z(beta,nu) = 2.14, 2.05 and 2 + epsilon2/75.1, while z(rho,beta,nu) = 2.17(4) and 2.04(4); both sets of values are in fair agreement with the literature.