arXiv subjects

Muktish Acharyya

Publications and source records attributed to Muktish Acharyya.

At least 37 records · Page 2Linked to original sources

arXiv2023

Effects of geometry, boundary condition and dynamical rules on the magnetic relaxation of Ising ferromagnet

We have studied the magnetic relaxation behavior of a two-dimensional Ising ferromagnet by Monte Carlo simulation. Our primary goal is to investigate the effects of the system's geometry (area preserving) , boundary conditions, and dynamical rules on the relaxation behavior. The Glauber and Metropolis dynamical rules have been employed. The systems with periodic and open boundary conditions are studied. The major findings are the exponential relaxation and the dependence of relaxation time ($τ$) on the aspect ratio $R$ (length over breadth having fixed area). A power law dependence ($τ\sim R^{-s}$) has been observed for larger values of aspect ratio ($R$). The exponent ($s$) has been found to depend linearly ($s=aT+b$) on the system's temperature ($T$). The transient behaviours of the spin-flip density have been investigated for both surface and bulk/core. The size dependencies of saturated spin-flip density significantly differ for the surface and the bulk/core. Both the saturated bulk/core and saturated surface spin-flip density was found to follow the logarithmic dependence $f_d = a + b~log(L)$ with the system size. The faster relaxation was observed for open boundary condition with any kind (Metropolis/Glauber) of dynamical rule. Similarly, Metropolis algorithm yields faster relaxation for any kind (open/periodic) of boundary condition.

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arXiv2023

Critical Slowing Down along the Separatrix of Lotka-Volterra Model of Competition

The Lotka-Volterra model of competition has been studied by numerical simulations using the Runge-Kutta-Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The transient behaviours associated with reaching the stable fixed point are studied systematically. It is observed that the time of reaching the stable fixed point in any one of the basins of attraction, depends strongly on the initial distance from the separatrix. As the initial point approached the separatrix, this time was found to diverge logarithmically. The divergence of the time, required to reach the stable fixed point, indicates the critical slowing down near the critical point in equilibrium phase transition. A metastable behaviour was also observed near the saddle fixed point before reaching the stable fixed point.

q-bio.PE↗

arXiv2022

Transient behavior of damage spreading in the two-dimensional Blume-Capel ferromagnet

We study the transient behavior of damage propagation in the two-dimensional spin-$1$ Blume-Capel model using Monte Carlo simulations with Metropolis dynamics. We find that, for a particular region in the second-order transition regime of the crystal field--temperature phase diagram of the model, the average Hamming distance decreases exponentially with time in the weakly damaged system. Additionally, its rate of decay appears to depend linearly on a number of Hamiltonian parameters, namely the crystal field, temperature, applied magnetic field, but also on the amount of damage. Finally, a comparative study using Metropolis and Glauber dynamics indicates a slower decay rate of the average Hamming distance for the Glauber protocol.

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arXiv2022

Theoretical studies on switching of magnetisation in thin film

In the present chapter, we focus on the switching of magnetisation, or the metastable lifetime of a ferromagnetic system. In this regard, particularly the Ising model and the Blume-Capel model, have been simulated in the presence of an externally applied magnetic field by the Monte-Carlo simulation technique based on the Metropolis algorithm. Magnetisation switching is found to be faster in the presence of disorder, modelled here by a quenched random field. The strength of the random field is observed to play a similar role to that played by temperature. Becker-Döring theory of classical nucleation (originally proposed for the spin-1/2 Ising system) has been verified in the random field Ising model. However, a stronger random field affects the nucleation regime. In a cubic Ising lattice, surface reversal time is found to be different from the bulk reversal time. That distinct behaviour of the surface in contrast to the bulk has been studied here by introducing a relative interfacial interaction strength ($R$). Depending on $R$, temperature, and applied field, a competitive switching of magnetisation of surface and bulk is noticed. The effect of anisotropy ($D$) on the metastable lifetime has been investigated. We report a linear dependency of the mean macroscopic reversal time on a suitably defined microscopic reversal time. The saturated magnetisation $M_f$, after the reversal, is noticed to be strongly dependent on $D$. $M_f$, $D$, and $h$ (field) are found to follow a proposed scaling relation. Finally, Becker-Döring theory as well as Avrami's law are verified in spin-$s$ Ising and Blume-Capel models. The switching time depends on the number of accessible spin states.

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arXiv2022

Monte Carlo study of the phase diagram of layered XY antiferromagnet

The three-dimensional XY model is investigated in the presence of a uniform magnetic field applied in the $X$-direction. The nearest neighbour intraplanar interaction is considered ferromagnetic, and the interplanar nearest neighbour interaction is chosen to be antiferromagnetic. Starting from a high-temperature initial random spin configuration, the equilibrium phase of the system at any finite temperature was achieved by cooling the system using the Monte Carlo single spin-flip Metropolis algorithm with a random updating rule. The components of total magnetisation and the sublattice magnetisations were calculated. The variance of the antiferromagnetic order parameter and the susceptibility have been calculated. In a specific range of relative strengths of interactions (antiferromagnetic/ferromagnetic) and the applied magnetic field, the system shows the equilibrium phase transitions at different temperatures. The phase diagrams (in the field-temperature plane) were obtained for different values of the relative interaction strengths. The ordered region bounded by the phase boundary was found to increase as the ratio of relative interaction strength increased. Furthermore, the maximum value of the susceptibility ($χ^m_{ay}$) was found to increase with the system size ($L$). For $χ^m_{ay} \sim L^{γ \over ν}$, the exponent $γ/ν$ has been estimated to be 2.10$\pm0.11$ .

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arXiv2022

Rodlike Heisenberg nanomagnet driven by propagating magnetic field: Nonequilibrium phase transition

The dynamical responses of a rodlike anisotropic Heisenberg ferromagnet, irradiated by the propagating magnetic field wave, have been studied by Monte Carlo simulation using Metropolis single spin-flip algorithm. A nonequilibrium dynamical phase transition has been observed. The transition temperature has been obtained from the peak position of the variance of the dynamic order parameter plotted as a function of the temperature. The transition has been found to occur at a lower temperature for the higher value of the amplitude of the propagating magnetic field wave. A comprehensive phase boundary was drawn. The phase boundary has been found to be insensitive to the wavelength of the propagating field wave. The boundary encloses more area of the region of the ordered phase for stronger anisotropy.

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arXiv2021

Modelling the Spread of an Epidemic in Presence of Vaccination using Cellular Automata

The results of Kermack-McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like SIR model. The motion of the circular front of an infected cluster shows a linear behaviour in time. The correlation of a particular site to be infected, with respect to the central site is also studied. The outcomes of CA model are in good agreement with that obtained from SIR model. The results of vaccination have been also incorporated in the CA algorithm with a satisfactory degree of success. The advantage of the present model is that it can shed considerable amount of light to the physical properties of the spread of a typical epidemic in a simple, yet robust way.

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arXiv2021

Metastable behavior of the spin-s Ising and Blume-Capel ferromagnets: A Monte Carlo study

We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of spin-$s$ Ising and Blume-Capel models, where $s=\{1/2, 1, 3/2, 2, 5/2, 3, 7/2\}$. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field and for both models is found to obey the Becker-Doring theory, as was initially developed for the case of $s=1/2$ Ising ferromagnet within the classical nucleation theory. Moreover, the decay of metastable volume fraction nicely follows the Avrami's law for all values of $s$ and for both models considered.

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arXiv2021

Competitive metastable behaviours of surface and bulk in Ising ferromagnet

The reversal of magnetisation has been studied in a three dimensional Ising ferromagnet by Monte Carlo simulation with Metropolis single spin flip algorithm using random updating scheme. The outer layers are considered as surface. The surface interacts with core with a relative ferromagnetic interaction strength. Depending on the relative interaction strength, the time of reversal of the surface was found to be different from that of the bulk. For weaker relative strength, surface reversal was found to be faster than that of bulk and vice versa for stronger relative interaction strength. A critical value ($R_c$) of relative interaction strength provides same time of reversal of surface and bulk. This critical relative interaction strength was found to be a function of the temperature ($T$) and applied magnetic field ($h$). The scaling relation $R_c \sim h^{-β}f(Th^α)$, where, $α=0.23\pm0.01$ and $β= -0.06\pm0.01$, has been proposed, numerically by the method of data collapse. The metastable volume fractions, for both surface and bulk, were found to follow the Avrami's law. The critical relative interaction strength ($R_c$) has been observed to decrease in an exponential ($e^{bL^{-1.5}})$ fashion with the system size ($L$).

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arXiv2021

Phase transition in Kermack-McKendrick Model of Epidemic: Effects of Additional Nonlinearity and Introduction of Medicated Immunity

Mathematical modelling of the spread of epidemics has been an interesting challenge in the field of epidemiology. The SIR Model proposed by Kermack and McKendrick in 1927 is a prototypical model of epidemiology. However, it has its limitations. In this paper, we show two independent ways of generalizing this model, the first one if the vaccine isn't discovered or ready to use and the next one, if the vaccine is discovered and ready to use. In the first part, we have pointed out a major over-simplification, i.e., assumption of variation of the time derivatives of the variables with the linear or quadratic powers of the individual variables and introduce two new parameters to incorporate further nonlinearity in the number of infected people in the model. As a result of this, we show how this additional nonlinearity, in the newly introduced parameters, can bring a significant shift in the peak time of infection, i.e., the time at which the infected population reaches maximum. We show that in special cases, even we can get a transition from epidemic to a non-epidemic stage of a particular infectious disease. We further study one such special case and treat it as a problem of phase transition. Then, we investigate all the necessary parameters of this phase transition, like the order parameter and critical exponent. We observe that $O_p \sim (q_c-q)^β$. {\it As far as we know the phase transition and its quantification in terms of the scaling behaviour is not yet know in the context of pandemic}. In the second part, we incorporate in the model, a consideration of artificial herd immunity and show how we can decrease the peak time of infection with a subsequent decrease in the maximum number of infected people.

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arXiv2021

Compensation in the spin-1/2 site diluted Ising ferrimagnet: A Monte Carlo study

A two-dimensional spin-1/2 trilayer magnetic system with quenched non-magnetic impurity is studied. The lattice is formed by alternate layers of two different theoretical atoms A and B arranged in a particular fashion A-B-A. The compensation point appears below the critical temperature, for which total magnetization of the system becomes zero even though the sublattice magnetization has a nonzero value. For a range of values of the relative interaction strength in the Hamiltonian, a compensation point is observed. We considered the Ising mechanics and employed the Monte Carlo method to determine the compensation point and critical temperature of the system. However, the effects of impurity in such systems are still not well studied. With that in mind, we address the effects of random non-magnetic impurity in the trilayer system. We also investigate the lattice morphologies in the presence of compensation and dilution and finally obtain the three-dimensional phase diagram for selected Hamiltonian parameters and impurity concentration.

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arXiv2021

Anisotropy driven reversal of magnetisation in Blume-Capel ferromagnet: A Monte Carlo study

The two dimensional Spin-1 Blume-Capel ferromagnet is studied by Monte Carlo simulation with Metropolis algorithm. Starting from initial ordered spin configuration the reversal of magnetisation is investigated in presence of a magnetic field ($h$) applied in the opposite direction. The variations of the reversal time with the strength of single site anisotropy are investigated in details. The exponential dependence was observed. The systematic variations of the mean reversal time with positive and negative anisotropy was found. The mean macroscopic reversal time was observed to be linearly dependent on a suitably defined microscopic reversal time. The saturated magnetisation $M_f$ after the reversal was noticed to be dependent of the strength of anisotropy $D$. An interesting scaling relation was obtained, $|M_f| \sim |h|^βf(D|h|^{-α})$ with the scaling function of the form $f(x)= \frac{1}{1+e^{(x-a)/b}}$. The temporal evolution of density of $S_i^z=0$ (surrounded by all $S_i^z=+1$) is observed to be exponentially decaying. The growth of mean density of $S_i^z=-1$ has been fitted in a function $ρ_{-1}(t) \sim \frac{1}{a+e^{(t_c-t)/c}}$. The characteristic time shows $t_c \sim e^{-rD}$ and a crossover in the rate of exponential falling is observed at $D=1.5$. The metastable volume fraction has been found to obey the Avrami's law.

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arXiv2020

Nonequilibrium Multiple Transitions in the Core-shell Ising Nanoparticles Driven by Randomly Varying Magnetic Fields

The nonequilibrium behaviour of a core-shell nanoparticle has been studied by Monte- Carlo simulation. The core consists of Ising spins of $σ=1/2$ and the shell contains Ising spins of $S=1$. The interactions within the core and in the shell are considered ferromagnetic but the interfacial interaction between core and shell is antiferromagnetic. The nanoparticle system is kept in open boundary conditions and is driven by randomly varying (in time but uniform over the space) magnetic field. Depending on the width of the randomly varying field and the temperature of the system, the core, shell and total magnetization varies in such a manner that the time averages vanish for higher magnitude of the width of random field, exhibiting a dynamical symmetry breaking transitions. The susceptibilities get peaked at two different temperatures indicating nonequilibrium multiple transitions. The phase boundaries of the nonequilibrium multiple transitions are drawn in the plane formed by the axes of temperature and the width of the randomly varying field. Furthermore, the effects of the core and shell thicknesses on the multiple transitions have been discussed.

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arXiv2020

Transient behaviour towards the stable limit cycle in the Selkov model of Glycolysis: A physiological disorder

A simplified model for the complex glycolytic process was historically proposed by Selkov. It showed the existence of stable limit cycle as an example of Poincare-Bendixson theorem. This limit cycle is nothing but the time eliminated Lissajous plot of the concentrations of Adenosine-diphosphate (ADP) and Fructose-6-phosphate (F6P) of a normal/healthy human. Deviation from this limit cycle is equivalent to the deviation of normal physiological behaviour. It is very important to know how long a human body will take to reach the glycolytic stable limit cycle, if deviated from it. However, till now the convergence time, depending upon different initial parameter values, was not studied in detail. This may have great importance in understanding the recovery time for a diseased individual deviated from normal cycle. Here the convergence time for different initial conditions has been calculated in original Selkov model. It is observed that convergence time, as a function of the distance from the limit cycle, gets saturated away from the cycle. This result seems to be a physiological disorder. A possible mathematical way to incorporate this in the Selkov model, has been proposed.

q-bio.QM↗

arXiv2020

Metastability in graded and step like variation of field and anisotropy of the Blume-Capel ferromagnet

The metastable behaviour of two dimensional anisotropic Blume-Capel ferromagnet, under the influence of graded and stepped like variations of magnetic field, has been investigated by extensive Monte Carlo simulation using Metropolis single spin flip algorithm. Starting from the initial perfectly ordered state, reversal of magnetisation has been studied in presence of the field. Metastable lifetime or the reversal time of magnetisation for the system having uniform anisotropy and in the presence of both graded and stepped field has been studied. Also the same has been explored for a {\it graded and stepped anisotropic system} in presence of a uniform field. Finite size effect is analyzed for the variation of reversal time with gradient of field ($G_h$) and a scaling relation $\langle τ\rangle \sim L^{-β} f(G_h L^α)$ is proposed. Spatial variation of density profile for the projection states (i.e., +1, 0 and -1) has also been studied at the moment of reversal of magnetisation. The spatial variation of the number of spin flips per site is studied. Motion of the interface (or domain wall) with the gradient of field and gradient of anisotropy are investigated and are found to follow the hyperbolic tangent like behaviours in both cases. Since, both the anisotropy and the applied field have significant impact on the metastable lifetime, an interesting competitive scenario is observed for a {\it graded anisotropic system in graded field} and a {\it stepped anisotropic system in stepped field}. A line of marginal competition has been found out for both the cases separating the regions of field dominated reversal and anisotropy dominated reversal. The decay of the metastable volume fraction was found to follow the Avrami's law. The mean reversal time was observed to decrease monotonically across the phase boundary of the ferro-para transition.

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arXiv2020

Role of anisotropy to the compensation in the Blume-Capel trilayered ferrimagnet

The trilayered Blume-Capel ($S=1$) magnet with nearest neighbour intralayer ferromagnetic and nearest neighbour interlayer antiferromagnetic interaction is studied by Monte Carlo simulation. Depending on the relative interaction strength and the value of anisotropy the critical temperature (where all the sublattice magnetisations and consequently the total magnetisation vanishes) and the compensation temperature (where the total magnetisation vanishes for a special combination of nonzero sublattice magnetisations) are estimated. The comprehensive phase diagrams with lines of critical temperatures and compensation temperatures for different parameter values are drawn.

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arXiv2020

Effects of random fields on the reversal of magnetisation of Ising ferromagnet

We have studied the reversal time of the magnetisation in two dimensional Ising ferromagnet in the presence of externally applied uniform magnetic field using Monte Carlo simulation based on Metropolis single spin flip algorithm. Then we have investigated the change in reversal time due to the presence of quenched random field in addition to the uniform magnetic field. We report the results of statistical distribution of reversal times in the presence of three different types of the distributions (namely, uniform, bimodal and normal) of random fields and compared the results with those obtained for uniform field only. We have observed that the reversal time decreases due to the presence of any kind (of distribution) of the random fields. The metastable volume fraction is observed to follow the Avrami's law. Dependence of reversal times on temperature and different widths of the distributions of random fields are also reported. We have also checked whether the system obeyed Becker-Doring theory of classical nucleation in presence of additional random field and tried to investigate the range of the width of the distribution of random field. For larger width of the distribution of random field, the system fails to show the reversal via the nucleation of a single droplet (for small values of uniform field only). The possible reason is analysed.

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arXiv2019

A Monte Carlo Study on the Variation of Residual Magnetisation with the Ratio of Coupling Strengths and Non-magnetic Impurities in an Ising Trilayer

We have studied a spin-1/2, ABA, Ising trilayer system with two different types of interactions, in-plane ferromagnetic and out-of-plane anti-ferromagnetic, among the lattice sites, on different layers. In the pure case, devoid of any impurity, we employed Monte-Carlo method with single spin-flip Metropolis algorithm to find out the anti-ferromagnetic critical temperature (Néel temperature) and another lower temperature, called the compensation temperature, both with total magnetisation zero, in accordance with already established results for square lattice. Then non-magnetic impurities, (spin value= 0) were implanted on each layer at randomly picked sites and their concentration was increased in steps from 5% to 20%. The ratio of inter-planar anti-ferromagnetic to mid-layer ferromagnetic coupling strength as well as the ratio of top and bottom layer ferromagnetic to mid layer ferromagnetic coupling strength were also varied and Néel and compensation temperatures, both were observed shifting towards lower temperature values with increase in concentration of impurities in the lattice for any fixed ratio of different coupling strengths, in absence of any external magnetic field. In addition, the magnitude of the residual magnetisation i.e. the ratio of the peak value of the magnetisation in between Néel and compensation points and the saturated value of magnetisation, was also observed to vary with different values of controlling parameters.

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