Glauber dynamics in the Ising chain with random transition rates

М. А. Алиев

赵兴宇, 黄心茹, 樊小辉 +1 more

It was first proposed that an extended chain Ising (ECI) model contains the Ising chain model,single spin doublewell potentials and a pure phonon heat bath of a specific energy exchange with the spins.The extension method is easy to apply to high dimensional cases.Then the single spin-flip probability (rate) of the ECI model is deduced based on the Boltzmann principle and general statistical principles of independent events and the model is simplified to an extended chain Glauber-Ising (ECGI) model.Moreover,the relaxation dynamics of the ECGI model were simulated by the Monte Carlo method and a comparison with the predictions of the special chain Glauber-Ising (SCGI) model was presented.It was found that the results of the two models are consistent with each other when the Ising chain length is large enough and temperature is relative low,which is the most valuable case of the model applications.These show that the ECI model will provide a firm physical base for the widely used single spin-flip rate proposed by Glauber and a possible route to obtain the single spin-flip rate of other form and even the multi-spin-flip rate.

M. Santos, W. Figueiredo

We study the dynamical critical behaviour of a double chain of spins where we take into account short-range four-spin interactions. This system is exactly soluble only in the thermodynamical equilibrium. We use the initial response rate of the order parameter to establish a lower bound to the dynamical critical exponent z. We show that, for the one- and two-spin-flip Glauber transition rates, the exponent z depends on the microscopic details of the Hamiltonian, that is, the dynamical critical exponent appears non-universal. This type of non-universal behaviour has already been seen in the one-dimensional Ising model with non-uniform exchange interactions.

J. M. Nunes da Silva, Eduardo Lage

H. J. Hilhorst, Masuo Suzuki, B. U. Felderhof

Alan J. Bray

The equal-time correlation function is calculated at T=0 for the one-dimensional Ising model with Glauber dynamics. Random initial conditions, appropriate to a sudden quench from non-zero temperature, are imposed. Averaging over initial conditions yields the scaling form C(r, t)=f(r 2 /t). The scaling function is given by f(x)= integral 0 1 (dy/ pi )(y(1-y)) -1/2 exp(-x/4y), and is universal, i.e. independent of the probability distribution for the initial conditions.