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

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

The Sarbanes-Oxley Act and Fiduciary Duties

This article explores the implications of the Sarbanes-Oxley Act of 2002 for fiduciary duty analysis in corporate law. The article examines those provisions of the Act, and recent SEC, NYSE and NASDAQ rules, that most pointedly bear on corporate governance. The article develops in detail exactly how Sarbanes-Oxley and those rules may alter state fiduciary duty law. Sarbanes-Oxley makes unprecedented federal inroads into the area of corporate governance and, although the fact of federal incursion into corporate governance is important in its own right, the more intriguing issue concerns the eventual interplay between federal and state law. Specifically, on various subjects will federal law wholly supplant, or merely supplement, state law? After first describing those recent regulatory initiatives most likely to raise fiduciary duty issues, we describe the fiduciary duties of directors, giving special attention to the emerging obligation of good faith, and highlight the often-overlooked fiduciary status of corporate officers. We note critical differences between breach of fiduciary duty claims against corporate officers and such claims against directors. We identify those few specific areas where Sarbanes-Oxley pre-empts inconsistent (and weaker) state fiduciary concepts, either in whole or in part. We also identify areas where the mandates of Sarbanes-Oxley, though lacking pre-emptive force, will be highly influential in state fiduciary duty analysis. We conclude, however, that state law will remain preeminent in the fiduciary duty area. This is because state law remains the lingua franca into which the mandates of Sarbanes-Oxley must inevitably be translated for fiduciary duty purposes. We therefore reject the view that Sarbanes-Oxley has somehow federalized the area of corporate fiduciary duty law. To be sure, federal law now plays a more significant role in corporate governance. The overall result of Sarbanes-Oxley in the corporate fiduciary duty area, however, is greater federal influence in a federalism arrangement in which fiduciary duties remain rooted in and dominated by state law

Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures

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

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.