Glauber dynamics

It should be realized that unlike the study of equilibrium thermodynamics for which a model is often mapped onto Ising system, elementary mechanism of atomic motion plays a deterministic role in the kinetic study. In an actual alloy system, diffusion of an atomic species is mainly driven by vacancy mechanism. The incorporation of the vacancy mechanism into PPM formalism, however, is not readily achieved, since the abundant freedom of microscopic path of atomic movement demands intractable number of variational parameters. The present study is, therefore, limited to a simple spin kinetics, known as Glauber dynamics [14] for which flipping events at fixed lattice points drive the phase transition. Hence, the present study for a spin system is regarded as a precursor to an alloy kinetics. The limitation of the model is critically examined and pointed out in the subsequent sections. 

The case of D / / 1 corresponds to the classicallsing model, whose dynamics was theoretically investigated in the 1960s by Glauber [8]. The main feature of Glauber dynamics is an exponential divergence of the relaxation time at low temperatures ... 

Coulon, C., Clerac, R., Lecren, L., Wemsdorfer, W., and Miyasaka, H. (2004) Glauber dynamics in a singlechain magnet from theory to real systems. Physical Review B Condensed Matter, 69, 132408. 

The formulation of the path probability function entirely depends on the kinetics assumed in the study. The vacancy-mediated kinetics or the exchange kinetics(Kawasaki dynamics ) requires a large number of path variables which make numerical operations intractable. The spin flipping kinetics(Glauber dynamics ) generally does not conserve the species with time, however the conservation is assured at 1 1 stoichiometric composition without imposing any additional constraints. In this regard, the spin system... 

This only depends on the probability of the termini, the total adiabatic works, and the total weight of stochastic transitions. The first of these is for uncorrelated motion and is the one that occurs in Glauber or Kawasaki dynamics [75-78]. The last term is, of course, very sensitive to the specified trajectory and the degree to which it departs from the adiabatic motion. However, the stochastic transitions are the same on the forward and on the reverse trajectory, and the ratio of the probabilities of these is... 

So far we have not been able to treat chains with bond correlations in more than one dimension. The introduction of more detailed or realistic models of local conformational processes, such as those of Reneker34 or of Schatzki,35 has, therefore, not been feasible. We may remark that the theory of dielectric relaxation by Work and Fujita,36 which applies Glauber s methods25 to delayed (dynamic) correlations between chain dipoles, is also in essence a one-dimensional affair. 

A small number of defects can also have a drastic effect on dynamics at low temperature, when the correlation length becomes very large. The problem of finite size scaling has been discussed by J.H. Luscombe et al. in the frame of the single-spin-flip Glauber model [30]. For an open chain of size L = na (with... 

Monte-Carlo simulations of the equilibrium properties of the model are carried for a triangular lattice of 100 X 100 sites. The equilibrium is provided by a combination of Glauber (single-chain excitations) and Kawasaki dynamics (conserving the cholesterol content) [5]. Monte Carlo simulations allow for an accurate determination of thermal quantites like the isothermal compressibility ... 

The steady-state dynamics is assumed to be governed by a Kawasaki-type particle-vacancy NN pair-exchange mechanism inside the system combined with a Glauber-type particle creation/annihilation mechanism at the two edges A and B. Hence, neither the particle number nor the total energy are conserved quantities. This implementation corresponds to a canonical ensemble inside the lattice and a grand canonical ensemble at the edges. The total density is hence a dependent variable which has to be calculated. The dynamical processes are subject to the conventional Monte Carlo Metropolis criterion. ... 

---