Dynamic Behavior of the 1d Ising Ferromagnet with Long-range Interactions

D. E. RODRIGUEZ; M. A. BAB; E. V. ALBANO

Punta del Este, Uruguay

Congreso; Medyfinol 2008; 2008

The dynamic behavior of the Ising model, with power-law decaying interactions of the form 1/r^(d+sigma), is simulated in d = 1 dimension for sigma = 0.75, by using the Monte Carlo method. This value of s is selected because we expect that critical exponents will be far from both the mean-field values (sigma= 0.5) and the strong Kosterlitz-Thouless behavior. Both the standard relaxation of ordered configurations and the short-time dynamics of disordered configurations are studied and rationalized in terms of scaling arguments. By measuring the time dependence of physical observables, such as the magnetization, susceptibility, Binder cumulant, correlation function, etc, the critical temperature and all the relevant critical exponents can be determined, including the static (beta, nu, and gamma) and the dynamic (z) ones. Also, the scaling exponent of the initial increase of the magnetization (theta) is evaluated. Based on this evidence we conclude that the study of the dynamic behavior of the system allows the complete characterization of its critical properties.