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Form Invariant Sommerfeld Electrical Conductivity in Generalised d Dimensions

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Communications in Theoretical Physics 2011年第11期56卷 943-944页

作者： muktish acharyya Department of Physics Presidency University

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 s... 详细信息

关键词：电导率尺寸 Boltzmann 菲动力学方法数学形式导电性

Reversal of Magnetisation in Ising Ferromagnet by the Field Having Gradient

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Communications in Theoretical Physics 2016年第11期65卷 563-570页

作者： Abyaya Dhar muktish acharyya Department of Physics Presidency University

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.

关键词：梯度场铁磁体磁化逆转蒙特卡洛模拟双曲正切函数平均寿命不连续性

Evidence of Invariance of Time Scale at Critical Point in Ising Meanfield Equilibrium Equation of State

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Communications in Theoretical Physics 2011年第6期55卷 1109-1112页

作者： muktish acharyya Ajanta Bhowal acharyya Department of Physics Presidency University86/1 College Street Calcutta-700073India Department of Physics Lady Brabourne CollegeP-1/2 Suhrawardy AvenueCalcutta-700017India

我们解决 Ising 铁磁物质的状态的平衡 meanfield 方程(从 BraggWilliams 获得了理论) 由 NewtonRaphson 方法。重复的数字要求了得到一个会聚的答案(在指定精确性以内) 在任何特别温度，平衡， magnetisation 被观察尽最大努力分叉温... 详细信息

我们解决 Ising 铁磁物质的状态的平衡 meanfield 方程(从 BraggWilliams 获得了理论) 由 NewtonRaphson 方法。重复的数字要求了得到一个会聚的答案(在指定精确性以内) 在任何特别温度，平衡， magnetisation 被观察尽最大努力分叉温度接近批评价值的法律时尚。这作为批评慢下来被识别。代表也被估计。代表的这值与从分析答案获得了那相比。除这以外，数字结果也与展出同意的令人满意的度的一些试验性的结果相比。它从这研究被观察在批评的点的时间规模的不变性的信息在 Ising 铁磁物质的状态的 meanfield 平衡方程是在场的。

关键词：尺度不变性平衡方程临界点时间证据 Newton 数值模拟布拉格

Nonequilibrium Phase Transition in Spin-S Ising Ferromagnet Driven by Propagating and Standing Magnetic Field Wave

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Communications in Theoretical Physics 2017年第11期67卷 600-610页

作者： Ajay Halder muktish acharyya Department of Physics Presidency University

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 oscillate 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.

关键词： Ising model dynamic phase transition Monte-Carlo algorithm propagating wave standing wave

Inflection Point as a Manifestation of Tricritical Point on the Dynamic Phase Boundary in Ising Meanfield Dynamics

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Communications in Computational Physics 2008年第2期3卷 397-405页

作者： muktish acharyya Ajanta Bhowal acharyya Department of Physics Presidency College86/1 College StreetCalcutta-700073India Department of Physics Hooghly Mohsin CollegePO-ChinsurahDist-HooghlyIndia.

We studied the dynamical phase transition in kinetic Ising ferromagnetsdriven by oscillating magnetic field in meanfield approximation. The meanfield differentialequation was solved by sixth order Runge-Kutta-Felberg method. We calculatedthe transition temperature as a function of amplitude and frequency of oscillatingfield. This was plotted against field amplitude taking frequency as a parameter.As frequency increases the phase boundary is observed to become inflated. The phaseboundary shows an inflection point which separates the nature of the transition. Onthe dynamic phase boundary a tricritical point (TCP) was found, which separates thenature (continuous/discontinuous) of the dynamic transition across the phase boundary.The inflection point is identified as the TCP and hence a simpler method of determiningthe position of TCP was found. TCP was observed to shift towards high fieldfor higher frequency. As frequency decreases the dynamic phase boundary is observeto shrink. In the zero frequency limit this boundary shows a tendency to merge to thetemperature variation of the coercive field.

关键词： Ising model meanfield theory dynamic transition tricritical point.

Exit Probability and First Passage Time of a Lazy Pearson Walker: Scaling Behaviour

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Applied Mathematics 2016年第12期7卷 1353-1358页

作者： muktish acharyya Department of Physics Presidency University Calcutta India

The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution 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 . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .

关键词： Pearson Walker Lazy Random Walk Exit Probability First Passage Time Scaling

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

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Journal of Modern Physics 2015年第14期6卷 2021-2034页

作者： muktish acharyya Department of Physics Presidency University Calcutta India

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 continuum. In all cases, the diffusive nature of walker breaks down due to tiring which is quite obvious. In one-dimension, the distribution of the displacement 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 reduce 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 is almost insensitive to the tiring factor. The probability 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.

关键词： Return Probability Exit Probability First Passage Time

Statistics of Projected Motion in One Dimension of a D-Dimensional Random Walker

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Applied Mathematics 2018年第6期9卷 602-617页

作者： Jayeeta Chattopadhyay muktish acharyya Department of Physics Indian Institute of Science Bangalore India Department of Physics Presidency University Calcutta India

We are studying the motion of a random walker in generalised 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, by addressing this particular type of problem, it shows that the projected motion is diffusive irrespective of any dimension;however, the diffusion rate is changing inversely with dimensions. As a consequence, it can be predicted that for the one dimensional projected motion of infinite dimensional random walk, the diffusion rate will be zero. This is an interesting result, at least pedagogically, which implies that though in infinite dimensions there is diffusion, 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 generalised 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”.

关键词： Higher Dimensions Random Walk Projected Walk Renormalizing Factor Diffusive

Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave

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Applied Mathematics 2019年第7期10卷 568-577页

作者： Ajay Halder muktish acharyya Department of Physics Presidency University Kolkata India

The purpose of this work is to identify the universality class of the nonequilibrium phase transition in the two-dimensional kinetic Ising ferromagnet driven by propagating magnetic field wave. To address this issue, the finite size analysis of the nonequilibrium phase transition, in two-dimensional Ising ferromagnet driven by plane propagating magnetic wave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamic phase transition from a high temperature dynamically symmetric (propagating) phase to a low temperature dynamically symmetry-broken (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 ?and the dynamic susceptibility , we have estimated the critical exponents and ?(measured from the data read at the critical temperature obtained from Binder cumulant), and (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 and ), within the limits of statistical errors.

关键词： Ising Model Dynamic Phase Transition Monte-Carlo Simulation Propagating Wave Finite Size Analysis Critical Exponents Universality