Capillary Waves at Liquid/Vapor Interfaces: A Molecular Dynamics Simulation

Evidence for capillary waves at a liquid/vapor interface are presented from extensive molecular dynamics simulations of a system containing up to 1.24 million Lennard-Jones particles. Careful measurements show that the total interfacial width depends logarithmically on $L_\parallel$, the length of the simulation cell parallel to the interface, as predicted theoretically. The strength of the divergence of the interfacial width on $L_\parallel$ depends inversely on the surface tension $\gamma$. This allows us to measure $\gamma$ two ways since $\gamma$ can also be obtained from the difference in the pressure parallel and perpendicular to the interface. These two independent measures of $\gamma$ agree provided that the interfacial order parameter profile is fit to an error function and not a hyperbolic tangent, as often assumed. We explore why these two common fitting functions give different results for $\gamma$

Hysteresis loop areas in kinetic Ising models: Effects of the switching mechanism

Experiments on ferromagnetic thin films have measured the dependence of the hysteresis loop area on the amplitude and frequency of the external field, $A$=$A(H_{0},\omega)$, and approximate agreement with numerical simulations of Ising models has been reported. Here we present numerical and theoretical calculations of $A$ in the low-frequency regime for two values of $H_{0}$, which bracket a temperature and system-size dependent crossover field. Our previous Monte Carlo studies have shown that the hysteretic response of the kinetic Ising model is qualitatively different for amplitudes above and below this crossover field. Using droplet theory, we derive analytic expressions for the low-frequency asymptotic behavior of the hysteresis loop area. In both field regimes, the loop area exhibits an extremely slow approach to an asymptotic, logarithmic frequency dependence of the form $A \propto - [\ln (H_{0} \omega)]^{-1}$. Our results are relevant to the interpretation of data from experiments and simulations, on the basis of which power-law exponents for the hysteresis-loop area have been reported.Comment: 9 pages including 3 figures. Submitted as a manuscript for the 7th Joint MMM-Intermag conference. To be published in the Journal of Applied Physics and the IEEE Transactions on Magnetics. Contains 1 updated figure and revised tex

Kinetic Ising model in an oscillating field: Finite-size scaling at the dynamic phase transition

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices $\beta$, $\gamma$ and $\nu$.Comment: Accepted by Physical Review Letters. 9 page

Nonequilibrium phase transition in the kinetic Ising model: Is transition point the maximum lossy point ?

The nonequilibrium dynamic phase transition, in the kinetic Ising model in presence of an oscillating magnetic field, has been studied both by Monte Carlo simulation (in two dimension) and by solving the meanfield dynamical equation of motion for the average magnetization. The temperature variations of hysteretic loss (loop area) and the dynamic correlation have been studied near the transition point. The transition point has been identified as the minimum-correlation point. The hysteretic loss becomes maximum above the transition point. An analytical formulation has been developed to analyse the simulation results. A general relationship among hysteresis loop area, dynamic order parameter and dynamic correlation has also been developed.Comment: 8 pages Revtex and 4 Postscript figures; To appear in Phys. Rev.

Kinetic Ising System in an Oscillating External Field: Stochastic Resonance and Residence-Time Distributions

Experimental, analytical, and numerical results suggest that the mechanism by which a uniaxial single-domain ferromagnet switches after sudden field reversal depends on the field magnitude and the system size. Here we report new results on how these distinct decay mechanisms influence hysteresis in a two-dimensional nearest-neighbor kinetic Ising model. We present theoretical predictions supported by numerical simulations for the frequency dependence of the probability distributions for the hysteresis-loop area and the period-averaged magnetization, and for the residence-time distributions. The latter suggest evidence of stochastic resonance for small systems in moderately weak oscillating fields.Comment: Includes updated results for Fig.2 and minor text revisions to the abstract and text for clarit

Hysteresis and the dynamic phase transition in thin ferromagnetic films

Hysteresis and the non-equilibrium dynamic phase transition in thin magnetic films subject to an oscillatory external field have been studied by Monte Carlo simulation. The model under investigation is a classical Heisenberg spin system with a bilinear exchange anisotropy in a planar thin film geometry with competing surface fields. The film exhibits a non-equilibrium phase transition between dynamically ordered and dynamically disordered phases characterized by a critical temperature Tcd, whose location of is determined by the amplitude H0 and frequency w of the applied oscillatory field. In the presence of competing surface fields the critical temperature of the ferromagnetic-paramagnetic transition for the film is suppressed from the bulk system value, Tc, to the interface localization-delocalization temperature Tci. The simulations show that in general Tcd < Tci for the model film. The profile of the time-dependent layer magnetization across the film shows that the dynamically ordered and dynamically disordered phases coexist within the film for T < Tcd. In the presence of competing surface fields, the dynamically ordered phase is localized at one surface of the film.Comment: PDF file, 21 pages including 8 figure pages; added references,typos added; to be published in PR

Spatial stochastic resonance in 1D Ising systems

The 1D Ising model is analytically studied in a spatially periodic and oscillatory external magnetic field using the transfer-matrix method. For low enough magnetic field intensities the correlation between the external magnetic field and the response in magnetization presents a maximum for a given temperature. The phenomenon can be interpreted as a resonance phenomenon induced by the stochastic heatbath. This novel "spatial stochastic resonance" has a different origin from the classical stochastic resonance phenomenon.Comment: REVTex, 5 pages, 3 figure

Dynamic Magnetization-Reversal Transition in the Ising Model

We report the results of mean field and the Monte Carlo study of the dynamic magnetization-reversal transition in the Ising model, brought about by the application of an external field pulse applied in opposition to the existing order before the application of the pulse. The transition occurs at a temperature T below the static critical temperature T_c without any external field. The transition occurs when the system, perturbed by the external field pulse competing with the existing order, jumps from one minimum of free energy to the other after the withdrawal of the pulse. The parameters controlling the transition are the strength h_p and the duration Delta t of the pulse. In the mean field case, approximate analytical expression is obtained for the phase boundary which agrees well with that obtained numerically in the small Delta t and large T limit. The order parameter of the transition has been identified and is observed to vary continuously near the transition. The order parameter exponent beta was estimated both for the mean field (beta =1) and the Monte Carlo beta = 0.90 \pm 0.02 in two dimension) cases. The transition shows a "critical slowing-down" type behaviour near the phase boundary with diverging relaxation time. The divergence was found to be logarithmic in the mean field case and exponential in the Monte Carlo case. The finite size scaling technique was employed to estimate the correlation length exponent nu (= 1.5 \pm 0.3 in two dimension) in the Monte Carlo case.Comment: 13 pages, latex, 8 figure