Form invariant Sommerfeld electrical conductivity in generalised d dimensions

The Sommerfeld electrical conductivity is calculated in d dimensions following Boltzmann kinetic approach. At T=0, the mathematical form of the electrical conductivity is found to remain invariant in any generalised spatial (d) dimensions.Comment: To appear in Comm. Theo. Phys. (2011

Nonequilibrium Phase Transition in the Kinetic Ising model: Absence of tricritical behaviour in presence of impurities

The nonequilibrium dynamic phase transition, in the two dimensional site diluted kinetic Ising model in presence of an oscillating magnetic field, has been studied by Monte Carlo simulation. The projections of dynamical phase boundary (surface) are drawn in the planes formed by the dilution and field amplitude and the plane formed by temperature and field amplitude. The tricritical behaviour is found to be absent in this case.Comment: This paper is withdrawn due to some error

Model and Statistical Analysis of the Motion of a Tired Random Walker in Continuum

The model of a tired random walker, whose jump-length decays exponentially in time, is proposed and the motion of such a tired random walker is studied systematically in one, two and three dimensional contin- uum. In all cases, the diffusive nature of walker, breaks down due to tiring which is quite obvious. In one dimension, the distribution of the displace- ment of a tired walker remains Gaussian (as observed in normal walker) with reduced width. In two and three dimensions, the probability distribution of displacement becomes nonmonotonic and unimodal. The most probable displacement and the deviation reduces as the tiring factor increases. The probability of return of a tired walker, decreases as the tiring factor increases in one and two dimensions. However, in three dimensions, it is found that the probability of return almost insensitive to the tiring factor. The prob- ability distributions of first return time of a tired random walker do not show the scale invariance as observed for a normal walker in continuum. The exponents, of such power law distributions of first return time, in all three dimensions are estimated for normal walker. The exit probability and the probability distribution of first passage time are found in all three dimensions. A few results are compared with available analytical calculations for normal walker.Comment: 10 pages latex and 20 Latex figure

Polarised Electromagnetic wave propagation through the ferromagnet: Phase boundary of dynamic phase transition

The dynamical responses of ferromagnet to the propagating electromagnetic field wave passing through it are modelled and studied here by Monte Carlo simulation in two dimensional Ising ferromagnet. Here, the electromagnetic wave is linearly polarised in such a way that the direction of magnetic field is parallel to that of the magnetic momemts (spins). The coherent propagating mode of spin-clusters is observed. The time average magnetisation over the full cycle (time) of the field defines the order parameter of the dynamic transition. Depending on the value of the temperature and the amplitude of the propagating magnetic field wave, a dynamical phase transition is observed. The dynamic transition was detected by studying the temperature dependences of the dynamic order parameter, the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The phase boundaries of the dynamic transitions were drawn for two different values of the wave lengths of the propagating magnetic field wave. The phase boundary was observed to shrink (inward) for lower speed of propagation of the EM wave. The divergence of the releavant length scale was observed at the transition point.Comment: 15 pages Latex, 6 figure

Comparison of meanfield and Monte Carlo approaches to dynamic hysteresis in Ising ferromagnets

The dynamical hysteresis is studied in the kinetic Ising model in the presence of a sinusoidal magnetic field both by Monte Carlo simulation and by solving the dynamical meanfield equation for the averaged magnetisation. The frequency variations of the dynamic coercive field are studied below the critical temperature. In both the cases, it shows a power law frequency variation however it becomes frequency independent in the low frequency regime for the meanfield case.Comment: 7 pages Latex (including figs.

Standing spin wave mode in RFIM at T=0: Patterns and nonequilibrium phases

The dynamical responses of random field Ising model at zero temperature, driven by standing magnetic field wave, is studied by Monte Carlo simulation in two dimensions. The three different kinds of distribution of quenched random field are used here, uniform, bimodal and Gaussian. In all cases, three distinct dynamical phases were observed, namely, the pinned, structured and random. In the pinned phase no spin flip is observed. In the structured phase standing spin wave modes are observed. The random phase is shown no regular pattern. For a fixed value of the amplitude of the standing magnetic field wave, in the region of small quenched field, the system remains in a pinned phase. In the intermediate range of values of random field, a standing spin wave mode (structured phase) is observed. The regular pattern of this spin wave mode disappears for higher values of random field yielding a random phase. The comprehensive phase baundaries are drawn in all three cases. The boundary of pinned phase are analytically calculated for uniform and bimodal types of quenched random fields.Comment: 14 pages Late

Nonequilibrium Magnetisation Reversal by Periodic Impulsive Field in Ising Meanfield Dynamics

We studied the nonequilibrium magnetisation reversal in kinetic Ising ferromagnets driven by periodic impulsive magnetic field in meanfield approximation. The meanfield differential equation was solved by sixth order Runge-Kutta-Felberg method. The periodicity and strength of the applied impulsive magnetic field play the key role in magnetisation reversal. We studied the minimum strength of impulsive field required for magnetisation reversal at any temperature as a function of the periodicity of the impulsive field. In the high temperature and small period this is observed to be linear. The results are compared with that obtained from Monte Carlo simulation of a three dimensional Ising ferromagnet.Comment: To appear in Physica Scripta (2010

Nonequilibrium phase transition in the kinetic Ising model driven by propagating magnetic field wave

The two dimensional ferromagnetic Ising model in the presence of a propagating magnetic field wave (with well defined frequency and wavelength) is studied by Mone Carlo simulation. This study differs from all of the earlier studies done so far, where the oscillating magnetic field was considered to be uniform in space. The time average magnetisation over a full cycle (the time period) of the propagating magnetic field acts as the dynamic order parameter. The dynamical phase transition is observed. The temperature variation of the dynamic order parameter, the mean square deviation of the dynamic order parameter, the dynamic specific heat and the derivative of the dynamic order parameter are studied. The mean square deviation of the dynamic order parameter, dynamic specific heat show sharp maxima near the transition point. The derivative of dynamic order parameter shows sharp minimum near the transition point. The transition temperature is found to depend also on the speed of propagation of the magnetic field wave.Comment: To appear in Physica Scripta (2011

Monte Carlo study of dynamic phase transition in Ising metamagnet driven by oscillating magnetic field

The dynamical responses of Ising metamagnet (layered antiferromagnet) in the presence of a sinusoidally oscillating magnetic field are studied by Monte Carlo simulation. The time average staggered magnetisation plays the role of dynamic order parameter. A dynamical phase transition was observed and a phase diagram was plotted in the plane formed by field amplitude and temperature. The dynamical phase boundary is observed to shrink inward as the relative antiferromagnetic strength decreases. The results are compared with that obtained from pure ferromagnetic system. The shape of dynamic phase boundary observed to be qualitatively similar to that obtained from previous meanfield calculations.Comment: 12 pages latex, PC-12-2010, To appear in J. Mag. Mag. Mat. (2011

Random field Ising model swept by propagating magnetic field wave: Athermal nonequilibrium phase diagram

The dynamical steady state behaviour of the random field Ising ferromagnet swept by a propagating magnetic field wave is studied at zero temperature by Monte Carlo simulation in two dimensions. The distribution of the random field is bimodal type. For a fixed set of values of the frequency and wavelength of propagating magnetic field wave and the strength of the random field, four distinct dynamical steady states or nonequilibrium phases were identified. These four nonequilibrium phases are characterised by different values of structure factors. State of first kind, where all spins are parallel (up). The second one is, the propagating type, where the sharp strips formed by parallel spins are found to move coherently. The third one is also propagating type, where the boundary of the strips of spins is not very sharp. The fourth kind, shows no propagation of stripes of magnetic spins, forming a homogeneous distribution of up and down spins. This is disordered phase The appearance of these four dynamical phases or modes depends on the value of the amplitude of propagating magnetic field wave and the strength of random (static) field. A phase diagram has also been drawn, in the plane formed by the amplitude of propagating field and the strength of random field. It is checked that, the existence of these dynamical phases is neither a finite size effect nor a transient phenomenon.Comment: 13 pages Latex, To Appear in J. Magn. Magn. Mater. (2013