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Muktish Acharyya

Publications and source records attributed to Muktish Acharyya.

At least 55 records · Page 3Linked to original sources

Universality class of the nonequilibrium phase transition in two dimensional Ising ferromagnet driven by propagating magnetic field wave

The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamicphase transition from a high temperature dynamically symmetric ({\it propagating}) phase to a low temperature dynamically symmetry-broken ({\it pinned}) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes ($L$). From the finite size analysis of dynamic order parameter ($Q_L \sim L^{-{β \over ν}}$) and the dynamic susceptibility ($χ^{Q}_{L} \sim L^{γ \over ν}$), we have estimated the critical exponents $β/ν=0.146\pm0.025$ and $γ/ν=1.869\pm0.135$ (measured from the data read at the critical temperature obtained from Binder cumulant), and $γ/ν=1.746\pm0.017$ (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where $β/ν=1/8$ and $γ/ν=7/4$), within the limits of statistical errors.

cond-mat.stat-mech↗

Magnetisation reversal in Ising Ferromagnet by Thermal and Field gradients

We report the results of the magnetisation reversal in Ising ferromagnet having thermal and field gradients by Monte Carlo simulation. We have studied the distribution of reversal times for different values of thermal and field gradients and compared the results with those obtained for uniform temperature. The movement of the domain wall of distinct domains and the growth of roughness of domain wall have also been studied statistically. The role of competing thermal and field gradients, in the reversal mechanism, was also studied and a line of marginal competition was obtained.

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Driven spin wave modes in XY ferromagnet: Nonequilibrium phase transition

The dynamical responses of XY ferromagnet driven by linearly polarised propagating and standing magnetic field wave have been studied by Monte Carlo simulation in three dimensions. In the case of propagating magnetic field wave (with specified amplitude, frequency and the wavelength), the low temperature dynamical mode is a propagating spin wave and the system becomes structureless (or random) in the high temperature. A dynamical symmetry breaking phase transition is observed at a finite (nonzero) temperature. This symmetry breaking is confirmed by studying the statistical distribution of the angle of the spin vector. The dynamic nonequilibrium transition temperature was found to decrease as the amplitude of the propagating magnetic field wave increased. A comprehensive phase boundary is drawn in the plane formed by temperature and amplitude of propagating field wave. The phase boundary was observed to shrink (in the low temperature side) for longer wavelength of the propagating magnetic wave. In the case of standing magnetic field wave, the low temperature excitation is a standing spin wave which becomes structureless (or random) in the high temperature. Here also, like the case of propagating magnetic wave, a dynamical symmetry breaking nonequilibrium phase transition was observed. A comprehensive phase boundary is drawn. Unlike the case of propagating magnetic wave, the phase boundary does not show any systematic variation with the wavelength of the standing magnetic field wave. In the limit of vanishingly small amplitude of the field, the phase boundaries approach the recent Monte Carlo estimate of equilibrium transition temperature.

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Transient phases in the Vicsek model of flocking

The Vicsek model of flocking is studied by computer simulation. We confined our studies here to the morphologies and the lifetimes of transient phases. In our simulation, we have identified three distinct transient phases, namely, vortex phase, colliding phase and multi-domain phase. The mapping of Vicsek model to XY model in the $v \to 0$ limit prompted us to explore the possibility of finding any vortex kind of phases in the Vicsek model. We have obtained rotating vortex phase and measured the lifetime of this vortex phase. We have also measured the lifetimes of other two transient phases, i.e., colliding phase and multi-domain phase. We have measured the integrated lifetime ($τ_t$) of all these transient phases and studied this as function of density ($ρ$) and noise ($η$). In the low noise regime, we proposed here a scaling law $τ_t N^{-a} = F(ρN^{-b})$ where $F(x)$ is a scaling function like $F(x) \sim x^{-s}$. By the method of data collapse, we have estimated the exponents as $a=-0.110\pm0.010$, $b=0.950\pm0.010$ and $s=1.027\pm0.008$. The integrated lifetime $τ$ (defined in the text differently) was observed to decrease as the noise approaches the critical noise from below. This behaviour is quite unusual and contrary to the critical slowing down observed in the case of equilibrium phase transitions. We have provided a possible explanation from the time evolution of the distribution of the directions of velocities.

cond-mat.stat-mech↗

Nonequilibrium phase transition in spin-S Ising ferromagnet driven by Propagating and Standing magnetic field wave

The dynamical response of spin-S (S=1, 3/2, 2, 3) Ising ferromagnet to the plane propagating wave , standing magnetic field wave and uniformly oscillating field with constant frequency are studied separately in two dimensions by extensive Monte Carlo simulation. Depending upon the strength of the magnetic field and the value of the spin state of the Ising spin lattice two different dynamical phases are observed. For a fixed value of S and the amplitude of the propagating magnetic field wave the system undergoes a dynamical phase transition from propagating phase to pinned phase as the temperature of the system is cooled down. Similarly in case with standing magnetic wave the system undergoes dynamical phase transition from high temperature phase where spins oscillates coherently in alternate bands of half wavelength of the standing magnetic wave to the low temperature pinned or spin frozen phase. For a fixed value of the amplitude of magnetic field oscillation the transition temperature is observed to decrease to a limiting value as the value of spin S is increased. The time averaged magnetisation over a full cycle of the magnetic field oscillation plays the role of the dynamic order parameter. A comprehensive phase boundary is drawn in the plane of magnetic field amplitude and dynamic transition temperature. It is found that the phase boundary shrinks inwards for high value of spin state S. Also in the low temperature (and high field) region the phase boundaries are closely spaced.

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Cellular Automata Model of Synchronization in Coupled Oscillators

We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of integers chosen from a finite set and defined on a lattice with periodic boundary conditions. The integers undergo coupled dynamics over discrete time steps. Depending on the values of coupling strength and range of coupling, we observed interesting collective dynamical phases namely: asynchronous, where all the integers oscillate incoherently; synchronized, where all integers oscillate coherently and also other states of intermediate and time-dependent ordering. We have adapted conventional order parameters used in coupled oscillator systems to measure the amount of synchrony in our system. We have plotted phase diagrams of these order parameters in the plane of strength of coupling and the radius of coupling. The phase diagrams reveal interesting properties about the nature of the synchronizing transition. There are partially ordered states, where there are synchronized clusters which are shown to have a power law distribution of their sizes. The power law exponent is found to be independent of the system parameters. We also discuss the possibility of chimera states in this model. A criterion of persistence of chimera is developed analytically and compared with numerical simulation.

nlin.AO↗

Spin flip statistics and Spin wave interference patterns in Ising ferromagnetic films: A Monte Carlo study

The spin wave interference is studied in two dimensional Ising ferromagnet driven by two coherent spherical magnetic field waves by Monte Carlo simulation. The spin waves are found to propagate and interfere according to the classic rule of interference pattern generated by two point sources. The interference pattern of spin wave is observed in one boundary of the lattice. The interference pattern is detected and studied by spin flip statistics at high and low temperatures. The destructive interference is manifested as the large number of spin flips and vice versa.

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Dynamical Phase transitions in Kuramoto model with distributed Sakaguchi phase

In this numerical work we have systematically studied the dynamical phase transitions in the Kuramoto- Sakaguchi model of synchronizing phase oscillators controlled by disorder in the Sakaguchi phases. We find out the numerical steady state phase diagrams for quenched and annealed kinds of disorder in the Sakaguchi parameters using the conventional order parameter and other statistical quantities like strength of incoherence and discontinuity measures. We have also considered the correlation profile of the local order parameter fluctuations in the various identified phases. The phase diagrams for quenched disorder is qualitatively much different than those the global coupling regime. The order of various transitions are confirmed by a study of the distribution of the order parameter and its fourth order Binder cumulant across the transition for an ensemble of initial distribution of phases. For annealed type of disorder, in contrast to the case with the quenched disorder, the system is almost insensitive to the amount of disorder. We also elucidate the role of chimeralike states in the synchronizing transition of the system and study the effect of disorder on these states. Finally, we seek justification of our results from simulations guided by the Ott-Antonsen ansatz.

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Blume-Capel ferromagnet driven by propagating and standing magnetic field wave: Dynamical modes and nonequilibrium phase transition

The dynamical responses of Blume-Capel (S=1) ferromagnet to the plane propagating (with fixed frequency and wavelength) and standing magnetic field waves are studied sepa- rately in two dimensions by extensive Monte Carlo simulation. Depending on the values of temperature, amplitude of the propagating magnetic field and the strength of anisotropy, two different dynamical phases are observed. For a fixed value of anisotropy and the amplitude of the propagating magnetic field, the system undergoes a dynamical phase transition from a driven spin wave propagating phase to a pinned or spin frozen state as the system is cooled down. The time averaged magnetisation over a full cycle of the propagating magnetic field plays the role of the dynamic order parameter. A comprehensive phase diagram is plotted in the plane formed by the amplitude of the propagating wave and the temperature of the system. It is found that the phase boundary shrinks inward as the anisotropy increases. The phase boundary, in the plane described by the strength of the anisotropy and temperature, is also drawn. This phase boundary was observed to shrink inward as the field amplitude increases.

cond-mat.stat-mech↗

Statistics of Projected Motion in one dimension of a d-dimensional Random Walker

We are studying the motion of a random walker in generalized d dimensional continuum with unit step length (up to 10 dimensions) and its projected one dimensional motion numerically. The motion of a random walker in lattice or continuum is well studied in statistical physics but what will be the statistics of projected one dimensional motion of higher dimensional random walker is yet to be explored. Here in this paper, addressing this particular type of problem, we have showed that the projected motion is diffusive irrespective of any dimension, however, the diffusion rate is changing inversely with dimension. As a consequence, we can say that at infinite dimension the diffusion rate becomes zero. This is an interesting result, at least pedagogically, which implies that though in infinite dimension there is a diffusion but its one dimensional projection is motionless. At the end of the discussion we are able to make a good comparison between projected one dimensional motion of generalized d-dimensional random walk with unit step length and pure one dimensional random walk with random step length varying uniformly between -h to h where h is a step length renormalizing factor.

cond-mat.stat-mech↗

Reversal of magnetisation in Ising ferromagnet by the field having gradient

We have studied the reversal of magnetisation in Ising ferromagnet by the field having gradient along a particular direction. We employed the Monte Carlo simulation with Metropolis single spin flip algorithm. The average lifetime of the metastable state was observed to increase with the magnitude of the gradient of applied field. In the high gradient regime, the system was observed to show two distinct region of up and down spins. The interface or the domain wall was observed to move as one increases the gradient. The displacement of the mean position of the interface was observed to increase with the gradient as hyperbolic tangent function. The roughness of the interface was observed to decay exponentially as the gradient increases. The number of spin flip per site was observed to show a discontinuity in the vicinity of the domain wall. The amount of the discontinuity was found to diverge with the system size as a power law fashion with an exponent 5/3.

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Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase transition

The dynamical response of an Ising ferromagnet to a plane polarised standing magnetic field wave is modelled and studied here by Monte Carlo simulation in two dimensions. The amplitude of standing magnetic wave is modulated along the direction x. We have detected two main dynamical phases namely, pinned and oscillating spin clusters. Depending on the value of field amplitude the system is found to undergo a phase transition from oscillating spin cluster to pinned as the system is cooled down. The time averaged magnetisation over a full cycle of magnetic field oscillations is defined as the dynamic order parameter. The transition is detected by studying the temperature dependences of the variance of the dynamic order parameter, the derivative of the dynamic order parameter and the dynamic specific heat. The dependence of the transition temperature on the magnetic field amplitude and on the wavelength of the magnetic field wave is studied at a single frequency. A comprehensive phase boundary is drawn in the plane described by the temperature and field amplitude for two different wavelengths of the magnetic wave. The variation of instantaneous line magnetisation during a period of magnetic field oscillation for standing wave mode is compared to those for the propagating wave mode. Also the probability that a spin at any site, flips, is calculated. The above mentioned variations and the probability of spin flip clearly distinguish between the dynamical phases formed by propagating magnetic wave and by standing magnetic wave in an Ising ferromagnet.

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Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity

We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for various types of collective states using the phase plots of the two statistical quantities, namely the strength of incoherence and the discontinity measure. In the quasi-static limit of the changing of coupling range, we have observed how the system relaxes from one state to another and have identified a few interesting collective dynamical states along the way. Under a sinusoidal change of the coupling range, the global order parameter characterizing the degree of synchronization in the system is shown to undergo a hysteresis with the coupling range. Finally, we study the low-dimensional spatio-temporal dynamics of the local order parameter in the continuum limit using the recently-developed Ott-Antonsen ansatz and justify some of our numerical results. In particular, we identify an intrinsic time-scale of the Kuramoto system and show that the simulations exhibit two distinct kinds of qualitative behavior in two cases when the time-scale associated with the switching of the coupling radius is very large compared to the intrinsic time-scale and when it is comparable with the intrinsic time-scale.

nlin.AO↗

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.

cond-mat.stat-mech↗

Exit probability and first passage time of a lazy Pearson walker: Scaling behaviour

The motion of a lazy Pearson walker is studied with different probability ($p$) of jump in two and three dimensions. The probability of exit ($P_e$) from a zone of radius $r_e$, is studied as a function of $r_e$ with different values of jump probability $p$. The exit probability $P_e$ is found to scale as ${P_e}p^α=F({r_e}p^β)$, which is obtained by method of data collapse. The first passage time ($t_1$) i.e., the time required for first exit from a zone is studied. The probability distribution ($P(t_1)$) of first passage time was studied for different values of jump probability ($p$). The probability distribution of first passage time was found to scale as ${P(t_1)}p^γ = G({t_1}p^δ)$. Where, $F$ and $G$ are two scaling functions and $α$, $β$, $γ$ and $δ$ are some exponents. In both the dimensions, it is found that, $α= 0$, $β=-1/2$, $γ=-1$ and $δ=1$.

cond-mat.stat-mech↗

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.

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Ising Metamagnet Driven by Propagating Magnetic Field Wave: Nonequilibrium Phases and Transitions

The nonequilibrium responses of Ising metamagnet (layered antiferromagnet) to the propagating magnetic wave are studied by Monte Carlo simulation. Here, the spatio-temporal variations of magnetic field keeps the system away from equilibrium. The sublattice magnetisations show dynamical symmetry breaking in the low temperature ordered phase. The nonequilibrium phase transitions are studied from the temperature dependences of dynamic staggered order parameter, its derivative and the dynamic specific heat. The transitions are marked by the peak position of dynamic specific heat and the position of dip of the derivative of dynamic staggered order parameter. It is observed that, for lower values of the amplitudes of the propagating magnetic field, if the system is cooled from a high temperature, it undergoes a phase transition showing sharp peak of dynamic specific heat and sharp dip of the derivative of the dynamic staggered order parameter. However, for higher values of the amplitude of the propagating magnetic field, system exhibits multiple phase transitions. A comprehensive phase diagram is also plotted. The transition, for vanishingly small value of the amplitude of the propagating wave, is very close to that for equilibrium ferro-para phase transition of cubic Ising ferromagnet.

cond-mat.stat-mech↗

Nucleation in the Ising ferromagnet by a field spatially spreading in time

The nucleation in Ising ferromagnet has been studied by Monte Carlo simulation. Here, the magnetic field is spreading over the space in time. The nucleation time is observed to increase as compared to that in the case of static field. The clusters of negative spins is observed to grow from the center. The growth of effective magnetisation is studied with temperature and the strength of spreading magnetic field. The ratio of nucleation time and effective time is also studied with strength of spreading magnetic field. The effective time would introduce itself as a new scale of time in the case of nucleation by spatially spreading magnetic field. The effective time and the nucleation time both are observed to decrease as a power law fashion with the rate factor of spreading magnetic field.

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