Ising model time-dependent

The time dependence of the dynamic correlation function q t) was investigated numerically on the Ising EA model by Ogielski [131], An empirical formula for the decay of q t) was proposed as a combination of a power law at short times and a stretched exponential at long times... 

Another model which includes interaction and for which partial results are available on the decay of initial correlations is that of the one dimensional time-dependent Ising model. This model was first suggested by Glauber,18 and analyzed by him for one-dimensional Ising lattices. Let us consider a one-dimensional lattice, each of whose sites contain a spin. The spin on site,/ will be denoted by s/t) where Sj(t) can take on values + 1, and transitions are made randomly between the two states due to interactions with an external heat reservoir. The state of the system is specified by the spin vector s(t) = (..., s- f), s0(t), Ji(0>---)- A- full description of the system is provided by the probability P(s t), but of more immediate interest are the reduced probabilities... 

Although the X/A - V diagram of Fig. 11 is less symmetric compared to that of Adam s Ising model, cf. Fig. 6, BEBBER (1975) has shown that the parameters of the A2-model can be chosen in such a way that its time-dependent excitation curve, i.e., the solution of (6.8), becomes almost indistinguishable from that of the Ising model. 

K. Kawasaki, Diffusion constants near the critical point for time-dependent ising models. I, Phys. Rev. 145, 224-230(1966). 

R, J. Glauber, Time-dependent statistics of the ising model, J. Math. Phys., 4, 294-307( 1953). 

There is a fundamental relationship between d-dimensional PCA and d + 1)-dimensional Ising spin models. The simplest way to make the connection is to think of the successive temporal layers of the PCA as successive hyper-planes of the next higher-dimensional spatial lattice. Because the PCA rules (at least the set of PCA rules that we will be dealing with) are (1) Markovian (i.e. the probability of a state at time t + T depends only on a set of states at time t, and (2) local, one can always define a Hamiltonian on the higher-dimensioned spatial lattice such that the thermodynamic weight of a configuration 5j,( is equal to the probability of a corresponding space-time history Si t). ... 

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