Numerical simulation of the critical dynamics of disordered 2D Ising systems

Svetislav Mijatović, Dragutin Jovković, Sanja Janićević +1 more

In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.

O. N. Markov, Vladimir V. Prudnikov

Hans-Otto Heuer

Gaurav Tenkila, Romain Vasseur, Andrew C. Potter

The edge of a quantum critical system can exhibit multiple distinct types of boundary criticality. We use a numerical real-space renormalization group (RSRG) to study the boundary criticality of a 2d quantum Ising model with random exchange couplings and transverse fields, whose bulk exhibits an infinite randomness critical point. This approach enables an asymptotically numerically exact extraction of universal scaling data from very large systems with many thousands of spins that cannot be efficiently simulated directly. We identify three distinct classes of boundary criticality, and extract key scaling exponents governing boundary-boundary and boundary-bulk correlations and dynamics. We anticipate that this approach can be generalized to studying a broad class of (disordered) boundary criticality, including symmetry-enriched criticality and edge modes of gapless symmetry-protected topological states, in contexts were other numerical methods are restricted to one-dimensional chains.

Jean Christian Anglès d’Auriac, R. Maynard, R. Rammal

Lei Xiao-wei

With dynamic Monte Carlo simulations,aging phenomena of two-dimensional Ising model and dynamic XY model were studied numerically.Systems were quenched to their critical point from a disordered initial state.The autocorrelation function was calculated by heat-bath algorithm.Critical exponents were also calculated.It was confirmed that for the 2D XY model,there is a logarithmic correction to scaling.The universality proposal and their scale relation in aging phenomena were predicted.The scale relation agreed with renormalization group calculations.