Effect of delayed interactions in the critical dynamics of the 1D Glauber model

Deepak Dhar, Mustansir Barma

Zhao‐Di Yang

In this work we study the Glauber dynamics of the one-dimensional Ising model with nearest-neighbor and next-nearest-neighbor interactions, for which an approximate solution of the magnetization per site is obtained. When the dynamical critical exponent z is investigated following the treatment of Cordery, Sarker, and Tobochnik [Phys. Rev. B 24, 5402 (1981)], our observation shows that its upper-bound value is the same as the known value, thus implying that z is independent of the range of the interaction. We also suggest a high-temperature expansion approximation which is then used to solve the two-dimensional Glauber dynamics governed by a master equation; this solution is compared with that of the decoupling method. The time-delayed correlation function is also calculated.

Eyal Lubetzky

Malte Henkel, Gunter Markus Schutz

The two-time nonequilibrium correlation and response functions in 1D kinetic classical spin systems with non-conserved dynamics and quenched to their zero-temperature critical point are studied. The exact solution of the kinetic Ising model with Glauber dynamics for a wide class of initial states allows for an explicit test of the universality of the non-equilibrium limit fluctuation-dissipation ratio X_{\infty}. It is shown that the value of X_{\infty} depends on whether the initial state has finitely many domain walls or not and thus two distinct dynamic universality classes can be identified in this model. Generic 1D kinetic spin systems with non-conserved dynamics fall into the same universality classes as the kinetic Glauber-Ising model provided the dynamics is invariant under the C-symmetry of simultaneous spin and magnetic-field reversal. While C-symmetry is satisfied for magnetic systems, it need not be for lattice gases which may therefore display hitherto unexplored types of non-universal kinetics.

J C Anglès d'Auriac, R. Rammal

It is shown that Glauber dynamics in 1D Ising spin systems is not universal. This is illustrated on a periodic model with a basic unit cell (J 1 ,. . ., J n ) containing an arbitrary set of n ferromagnetic coupling constants. The dynamic critical exponent z is calculated exactly as z=1+max(J i )/min(J i ), the known value z=2 is recovered only for n=1. The extension of this result to other types of dynamics is briefly discussed.

J. C. Niel, Jean Zinn‐Justin