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Muktish Acharyya

Publications and source records attributed to Muktish Acharyya.

At least 19 recordsLinked to original sources
arXiv2026

Compensation in continuous symmetric trilayered planar ferrimagnet

The trilayered (A-B-A type) anisotropic (single site) XY magnetic model is considered with the intra-plane ferromagnetic and the inter-plane antiferromagnetic interactions. The equilibrium properties of such trilayered anisotropic XY system has been studied by Monte Carlo simulation with Metropolis single spin (randomly chosen) update algorithm. In a given range of interaction parameters, the system has been found to exhibit the high temperature {\it critical} (vanishing sublattice magnetisations and total magnetisation) and low temperature {\it compensation} (vanishing total magnetisation even for non-vanishing sublattice magnetisations) behaviours. The compensation temperature and the critical temperature both are found to increase with the increase of single site anisotropy. The comprehensive phase diagram is drawn. The finite size study reveals the growth of correlations near the critical temperature.

cond-mat.stat-mech↗
arXiv2025

Multiple crossover in the decay of metastable volume fraction of a Blume-Capel ferromagnetic needle

The transient behaviours of a Blume-Capel ferromagnetic needle have been studied extensively by Monte-Carlo simulation. The needle has an elongated length in one direction compared to its cross-section. In the context of transient behaviour, we have captured the decay of the metastable state and the magnetic relaxation behaviours in our study. The dependence of metastable behaviour with anisotropy (single site) has been studied. \emph{Interestingly, we have observed multiple (different values of $n$ in different time domains) crossover in the decay of metastable volume fraction (obeying Avrami's law $β\sim {\rm exp}(-Kt^n)$). We have identified the crossover time, and the values of $n$ are estimated precisely.} The mean (magnetic) reversal time has been studied as a function of anisotropy. It is observed to be almost independent of anisotropy for its negative value; however, it is found to decrease exponentially with positive anisotropy. The exponential relaxation behaviour (in the corresponding paramagnetic phase) is observed. The relaxation time was found to depend on the strength of anisotropy.

cond-mat.stat-mech↗
arXiv2025

Compensation in trilayered anisotropic 6-state clock model

The equilibrium behaviours of a trilayered 6-state clock model have been investigated by Monte Carlo simulation. The intralayer interaction is considered ferromagnetic, whereas the interlayer interaction is antiferromagnetic. Periodic boundary conditions(PBC) are applied in XY plane and open boundary condition (OBC) is applied along Z-direction. The thermodynamic behaviours of sublattice magnetisation, total magnetisation, magnetic susceptibility and the specific heat are studied as functions of the temperature. The interesting compensation phenomenon, when the total magnetisation vanishes keeping the nonzero sublattice magnetisations, has been observed. The compensation temperature and the critical temperature are found to depend on the strength of single-site anisotropy. The comprehensive phase diagram is shown in the temperature-anisotropy plane. The larger systems show the growth of the height of the peak of the susceptibility near the critical temperature.

cond-mat.stat-mech↗
arXiv2025

deGennes-Suzuki-Kubo Quantum Ising Mean Field Dynamics: Applications to Quantum Hysteresis, Heat Engines and Annealing

We briefly review the early development of the mean-field dynamics for cooperatively interacting quantum many-body systems, mapped to pseudo-spin (Ising-like) systems. We start with (Anderson, 1958) pseudo-spin mapping of the BCS (1957) Hamiltonian of superconductivity, reducing it to a mean-field Hamiltonian of XY (or effectively Ising) model in a transverse field. Then we get the mean-field estimate for the equilibrium gap in the ground state energy at different temperatures (gap disappearing at the transition temperature), which fits Landau's (1949) phenomenological theory of superfluidity. We then present in detail a general dynamical extension (for non-equilibrium cases) of the mean-field theory of quantum Ising systems (in a transverse field), following de Gennes' (1963) decomposition of the mean field into orthogonal classical cooperative (longitudinal) component and the quantum (transverse) component, with each component following Suzuki--Kubo (1968) mean-field dynamics. Next we discuss its applications to quantum hysteresis in Ising magnets (in presence of an oscillating transverse field), to quantum heat engines (employing transverse Ising model as working fluid), and to the quantum annealing of the Sherrington--Kirkpatrick (1975) spin glass by tuning down (to zero) the transverse field, which provides a very fast computational algorithm leading to ground state energy values converging to the best known analytic estimate for the model. Finally, we summarize the main results obtained and conclude about the effectiveness of the de Gennes--Suzuki--Kubo mean-field equations for the study of various dynamical aspects of quantum condensed matter systems.

cond-mat.stat-mech↗
arXiv2025

Strange relaxation and metastable behaviours of the Ising ferromagnetic thick cubic shell

We have studied the equilibrium and nonequilibrium behaviours of the Ising ferromagnetic thick cubic shell by Monte Carlo simulation. Our goal is to find the dependence of the responses on the thickness of the shell. In the equilibrium results, we found that the pseudo-critical temperature of ferro-para phase transition of thick cubic shell increases with the increase of the thickness following a hyperbolic tangent relation. In the nonequilibrium studies, the relaxation time has been found to decrease with the increase of the thickness of the cubic shell. Here three different regimes are found, namely rapid fall, plateau and linear region. The metastable behaviour has been studied also as another kind of non-equilibrium response. The metastable lifetime has been studied as function of the thickness of the cubic shell. A non-monotonic variation of metastable lifetime with the thickness of the shell is observed. A specified thickness for longest-lived metastability has been identified.

cond-mat.stat-mech↗
arXiv2025

Role of Noise in the Fairen-Velarde model of bacterial respiration

Following our recent study (S. Kundu and M. Acharyya, International Journal of Modern Physics C, 35 (2024) 2450094), we have introduced stochasticity (random noise) in the Fairen-Velarde deterministic differential equations. The role of such noise on time scales is studied. The probability of reaching the domain of fixed points in a given interval is also calculated. The probability is studied as a function of the width of the noise, and a hyperbolic tangent fitting is proposed. The noise reduces the time scale for bringing the bacteria into an inactive state. The area of the fixed-point domain was found to be asympotically linear with noise. The time to reach the fixed-point domain is fitted to a Gaussian function with noise intensity.

q-bio.QM↗
arXiv2024

What will be the Euclidean dimension of an Ising ferromagnetic cubic shell?

The equilibrium and nonequilibrium properties of an Ising ferromagnetic cubic shell have been extensively studied by Monte Carlo simulation using Metropolis single spin flip algorithm. Although, geometrically the Euclidean dimension of the cubical shell is three, interestingly, the Ising ferromagnetic cubic shell undergoes ferromagnetic phase transition at a temperature which is very close to that for two-dimensional Ising ferromagnet. Surprisingly, the Ising ferromagnetic cubic shell shows a strange (neither exponential nor stretched exponential) kind of relaxation behaviour, instead of exponential relaxation as usually observed in the two dimensional Ising ferromagnet. The metastable lifetime of a ferromagnetic Ising cubical shell is studied as a function of the applied magnetic field. Here also, the cubic shell behaves more likely a two-dimensional object as found from statistical analysis and comparison with Becker-Döring prediction of classical nucleation theory.

cond-mat.stat-mech↗
arXiv2024

Nonequilibrium tricritical behaviour in anisotropic XY ferromagnet driven by elliptically polarised propagating magnetic field wave

Three dimensional anisotropic XY ferromagnet driven by elliptically polarized propagating magnetic field wave has been extensively investigated by Monte Carlo simulation with Metropolis single spin flip algorithm. Both the effects of the bilinear exchange type and the single site anisotropies are thoroughly investigated. The time average magnetisation (over the complete cycle of the elliptically polarized propagating magnetic field wave) components play the role of dynamic order parameter. For fixed set of values of the strength of anisotropy and the field amplitudes, the system has been found to get dynamically ordered at a pseudocritical temperature. The pseudocritical temperature of such dynamic nonequilibrium phase transition has been found to depend on both the strength of anisotropy and the amplitudes of the elliptically polarized propagating magnetic field wave. A comprehensive phase diagram is represented here in the form of image plot of the pseudocritical temperature in the plane formed by the strength of anisotropy and field amplitudes. Interestingly, this nonequilibrium phase transition has been found discontinuous (first order) for higher values of the field amplitude and lower values of the anisotropy. On the other hand, the continuous (second order) transition has been noticed for lower values of the field amplitude and higher values of the anisotropy.

cond-mat.stat-mech↗
arXiv2024

Critical behaviours of anisotropic XY ferromagnet in the presence of random field

The anisotropic XY ferromagnet has been studied by Monte Carlo simulation in a three dimensional simple cubic lattice. The increase in critical temperature (ferro-para transition) has been noticed with increasing the strength of anisotropy. The effects of random fields (both with full circular symmetry and in angular window) on the critical temperature are investigated systematically in the anisotropic XY ferromagnet in three dimensions. Reduction in the critical temperature of anisotropic XY ferromagnet has been observed in the presence of random field. The compensating field (the required amount of field which preserves the critical temperature for isotropic XY ferromagnet) has been studied as a function of the strength of anisotropy. The compensating field was found to depend linearly on the strength of anisotropy. We have also studied the effects of random field confined in the angular window and observed the reduction of the critical temperature with increase of the angular extension. The critical behaviours are formalized by the usual finite size analysis and the estimation of critical exponents for the susceptibility and the specific heat. .

cond-mat.stat-mech↗
arXiv2024

Quantum Ising Heat Engines: A mean field study

We have studied the efficiencies of both classical and quantum heat engines using an Ising model as working fluid and the mean field equation for its non-equilibrium dynamics, formulated earlier\cite{acs,ac} to study the dynamical hysteresis and the dynamical phase transitions in the quantum Ising ferromagnets. We studied numerically the Ising magnet's nonintegrable coupled nonlinear first order differential equations of motion for a four stroke heat engine and compared the efficiencies in both classical and quantum limits using the quasi-static approximation. In both the pure classical and pure quantum cases, the numerically calculated efficiencies are much less than the corresponding Carnot values. Our analytical formulations of the efficiencies (both in pure classical as well as in pure quantum Ising heat engines) are found to agree well with the numerical estimates. Such formulations also indicate increased efficiency for the mixed case of a transverse field driven Ising engine in presence of nonzero longitudinal field. We also numerically checked and found that the efficiency of such a (mixed) quantum Ising heat engine can indeed have much higher efficiency for appropriate values of the transverse and longitudinal fields.

cond-mat.stat-mech↗
arXiv2024

Phase transitions in the anisotropic XY ferromagnet with quenched nonmagnetic impurity

The three dimensional anisotropic XY ferromagnet has been studied by Monte Carlo simulation. The ferro-para phase transition has been observed to take place at a lower temperature for impure anisotropic XY ferromagnet. The pseudocritical temperature ($T_c^*$) has been found to decrease as the system gets more and more impure (impurity concentration $p$ increases). In the case of bilinear exchange type of anisotropy ($λ$), the pseudocritical temperature ($T_c^*$) increases linearly with $λ$ for any given concentration of nonmagnetic impurity ($p$). The slope of this linear function has been found to depend on the impurity concentration ($p$). The slope decreases linearly with the impurity concentration ($p$). In the case of the single site anisotropy ($D$), the pseudocritical temperature ($T_c^*$) has been found to decrease linearly with $p$ for fixed $D$. The critical temperature (for a fixed set of parameter values) has been estimated from the temperature variation of fourth order Binder cumulants ($U_L$) for different system sizes ($L$). The critical magnetisation ($M(T_c)$) and the maximum value of the susceptibility ($χ_p$) are calculated for different system sizes ($L$). The critical exponents for the assumed scaling laws, $M(T_c) \sim L^{-{β \over ν}}$ and $χ_p \sim L^{γ \over ν}$, are estimated through the finite size analysis. We have estimated, ${β \over ν}$, equals to $0.48\pm0.05$ and $0.37\pm0.04$ for bilinear exchange and single site anisotropy respectively. We have also estimated, ${γ \over ν}$ equals to $1.78\pm0.05$ and $1.81\pm0.05$ for bilinear exchange and single site anisotropy respectively.

cond-mat.stat-mech↗
arXiv2023

Existence of two distinct time scales in the Fairen-Velarde model of bacterial respiration

We study the bacterial respiration through the numerical solution of the Fairen-Velarde coupled nonlinear differential equations. The instantaneous concentrations of the oxygen and the nutrients are computed. The fixed point solution and the stable limit cycle are found in different parameter ranges as predicted by the linearized differential equations. In a specified range of parameters, it is observed that the system spends some time near the stable limit cycle and eventually reaches the stable fixed point. This metastability has been investigated systematically. Interestingly, it is observed that the system exhibits two distinctly different time scales in reaching the stable fixed points. The slow time scale of the metastable lifetime near the stable limit cycle and a fast time scale (after leaving the zone of limit cycle) in rushing towards the stable fixed point. The gross residence time, near the limit cycle (described by a slow time scale), can be reduced by varying the concentrations of nutrients. This idea can be used to control the harmful metastable lifespan of active bacteria.

q-bio.PE↗
arXiv2023

Equilibrium and Nonequilibrium phase transitions in continuous symmetric classical magnets

The magnetism is an old problem of Physics. Most interesting part of the research on magnetism is its thermodynamic behaviour. In this review, the thermodynamic phase transitions, mainly in ferromagnetic model systems, are discussed. The model system has a characteristic of continuous symmetry. In this context, the classical XY and Heisenberg model are chosen for discussion. With a historical survey of such phase transition observed in such models, the results of the recent (over two decades) studies are collected and reviewed. The equilibrium phase transition in such systems are discussed to highlight the dependence of the critical temperatures on the anisotropy, dilution etc. On the other hand, the nonequilibrium results of such systems driven by time dependent magnetic field, are also reviewed. We believe, this review is a modern documentation and collection of works in the field of theoretical magnetism which may be extremely useful for the researcher working in this field.

cond-mat.stat-mech↗
arXiv2023

Relaxation behaviours in ferromagnetic monolayers

In this article, we briefly review the studies on magnetic relaxation behaviours. The theoretical as well as experimental investigations are reported briefly. A major part of this article is devoted to the recent Monte Carlo investigations into the roles of boundary conditions, dynamics and the Geometrical structures on the relaxation of magnetic monolayers modelled by two-dimensional Ising ferromagnet. We have studied all these effects for a two dimensional Ising system with two types of deformations, namely preserving and area non-preserving.The Glauber protocol and Metropolis dynamical rules are employed in our simulations and we investigated the systems with both periodic and open boundary conditions. The major findings are the exponential relaxation and the dependence of relaxation time ($τ$) on the aspect ratio $R$ (length over breadth). A power law dependence ($τ\sim R^{-s}$) has been observed for larger values of aspect ratio ($R$). The linear thermal ($T$) dependence of exponent ($s$) has been noticed ($s = aT + b$). The transient behaviours of the spin-flip density have also been studied here for both surface and bulk/core. Both the saturated bulk/core and saturated surface spin-flip density are observed to follow the logarithmic dependence $f_{d} = a + b~\log(L)$ with the system size ($L$). For open boundary condition with any kind (Metropolis/Glauber) of dynamical rule, the faster relaxation has been observed. Similarly, Metropolis algorithm yields faster relaxation for any kind (open/periodic) of boundary condition. We appeal to the experimentalists for experimental support which may be applied in judicious {\it magnetic coating} of the credit cards for quicker response.

cond-mat.stat-mech↗
arXiv2023

Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy

The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetization ($M$) and the susceptibility ($χ$) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws $M \sim L^{-{β \over ν}}$ and $χ\sim L^{γ \over ν} $ are estimated through the finite size analysis.

cond-mat.stat-mech↗
arXiv2023

Disorder effects on the metastability of classical Heisenberg ferromagnets

In the present work, we investigate the effects of disorder on the reversal time ($τ$) of classical anisotropic Heisenberg ferromagnets in three dimensions by means of Monte Carlo simulations. Starting from the pure system, our analysis suggests that $τ$ increases with increasing anisotropy strength. On the other hand, for the case of randomly distributed anisotropy, generated from various statistical distributions, a set of results is obtained: (i) For both bimodal and uniform distributions the variation of $τ$ with the strength of anisotropy strongly depends on temperature. (ii) At lower temperatures, the decrement in $τ$ with increasing width of the distribution is more prominent. (iii) For the case of normally distributed anisotropy, the variation of $τ$ with the width of the distribution is non-monotonic, featuring a minimum value that decays exponentially with the temperature. Finally, we elaborate on the joint effect of longitudinal ($h_z$) and transverse ($h_x$) fields on $τ$, which appear to obey a scaling behavior of the form $τh_z^{n} \sim f(h_x)$.

cond-mat.stat-mech↗
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.

cond-mat.stat-mech↗