Critical relaxation
(exponent z) is described by a reversible growth of clusters: Particles of a cluster are ordered into connected sequences, such that a stepwise variation of their length describes relaxation.
We derive z = z(p, p, V) where p is a scaling exponent relating cluster size to connected length at equilibrium, available from simulation of Ising clusters. Furthermore, a Flory-like equation gives p = p( /3, v), and hence z = z( p, v). In D = 2 and 3, theoretical z( p, V) an simulation-aided z( p, p, V) agree reasonably well with each other and with direct simulations of z. In D = 4 -E, z( p, V) agrees with the exact RG.
Particles with long-range correlation exhibit an exceedingly slow relaxation to thermal equilibrium. Relaxation time T of the order parameter ("model A" dynamics) diverges with the correlation length 5 as T -5'. RG [l] shows that z cannot be described with the sole help of static critical exponents, like /3 and V. Here, however, assuming a description of fluctuation dissipation by critical clusters, z is related to p, v', and to an additional exponent p; viz. z = z( p, /3, v), where p may be measured with the help of a simulation at equilibrium. Furthermore, a Flory-like equation enables us to relate p to p and V, leading to a closed equation z = z( p, v). The theory should also apply to dynamics of other reversibly connected clusters, like living polymers.