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Register a new userStochastic Resonance and Nonequilibrium Dynamic Phase Transition of Ising Spin System Driven by a Joint External Field
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We studied the dynamic response and stochastic resonance of kinetic Ising spin system (ISS), subject to the joint external field of weak sinusoidal modulation and stochastic white-noise, through solving the mean-field equation of motion based on Glauber dynamics. The periodically driven stochastic ISS shows the occurrence of characteristic stochastic resonance as well as nonequilibrium dynamic phase transition (NDPT) when the frequency and amplitude h0 of driving field, the temperature t of the system and noise intensity D attain a specific accordance in quantity. There exist in the system two typical dynamic phases, referred to as dynamic disordered paramagnetic and ordered ferromagnetic phases respectively, corresponding to zero and unit dynamic order parameter. We also figured out the NDPT boundary surface of the system which separates the dynamic paramagnetic and dynamic ferromagnetic phase in the 3D parameter space of h0~t~D. An intriguing dynamical ferromagnetic phase with an intermediate order parameter at 0.66 was revealed for the first time in the ISS subject to the perturbation of a joint determinant and stochastic field. Our primary result indicates that the intermediate order dynamical ferromagnetic phase is dynamic metastable in nature and owns a peculiar characteristic in its stability and response to external driving field when compared with fully order dynamic ferromagnetic phase.
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We report the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subject to the joint application of a deterministic external field and the stochastic mutually correlated noises simultaneously. A time-dependent Ginzburg-Landau stochastic differential equation, including an oscillating modulation and the correlated multiplicative and additive white noises, was addressed and the numerical solution to the relevant Fokker-Planck equation was presented on the basis of an average-period approach of driven field. The correlated white noises and the deterministic modulation induce a kind of dynamic symmetry-breaking order, analogous to the stochastic resonance in trend, in the kinetic ISS, and the reentrant transition has been observed between the dynamic disorder and order phases when the intensities of multiplicative and additive noises were changing. The dependencies of a dynamic order parameter Q upon the intensities of additive noise A and multiplicative noise M, the correlation lmda between two noises, and the amplitude of applied external field h were investigated quantitatively and visualized vividly. A brief discussion was given to outline the underlying mechanism of the NDPT in a kinetic ISS driven by an external force and correlated noises. Keywords: Ising spin system, nonequilibrium dynamical phase transition, stochastic resonance, correlated noises, TDGL model. PACS: 75.10.Hk, 64.60.Ht, 05.10.Gg, 76.20.+q
Dynamic behavior of a site diluted Ising ferromagnet in the presence of periodically oscillating magnetic field has been analyzed by means of the effective field theory (EFT). Dynamic equation of motion have been solved for a honeycomb lattice ($z=3$) with the help of a Glauber type stochastic process. The global phase diagrams and the variation of the corresponding dynamic order parameter as a function of the Hamiltonian parameters and temperature has been investigated in detail and it has been shown that the system exhibits reentrant phenomena, as well as a dynamic tricritical point which disappears for sufficiently weak dilution.
We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [P.A. Rikvold and M. Kolesik, J. Phys. A: Math. Gen. 35, L117 (2002)], for which both nucleation and interface propagation are slower and the interfaces smoother than for the standard Glauber dynamic. We choose the temperature and magnitude of the external field such that the metastable decay of the system following field reversal occurs through nucleation and growth of many droplets of the stable phase, i.e., the multidroplet regime. Using kinetic Monte Carlo simulations, we find that the system undergoes a nonequilibrium phase transition, in which the symmetry-broken dynamic phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. The critical point is located where the half-period of the external field is approximately equal to the metastable lifetime of the system. We employ finite-size scaling analysis to investigate the characteristics of this dynamical phase transition. The critical exponents and the fixed-point value of the fourth-order cumulant are found to be consistent with the universality class of the two-dimensional equilibrium Ising model. As this universality class has previously been established for the same nonequilibrium model evolving under the standard Glauber dynamic, our results indicate that this far-from-equilibrium phase transition is universal with respect to the choice of the stochastic dynamics.
The square-lattice Ising antiferromagnet subjected to the imaginary magnetic field $H=i theta T /2 $ with the topological angle $theta$ and temperature $T$ was investigated by means of the transfer-matrix method. Here, as a probe to detect the order-disorder phase transition, we adopt an extended version of the fidelity susceptibility $chi_F^{(theta)}$, which makes sense even for such a non-hermitian transfer matrix. As a preliminary survey, for an intermediate value of $theta$, we examined the finite-size-scaling behavior of $chi_F^{(theta)}$, and found a pronounced signature for the criticality; note that the magnetic susceptibility exhibits a weak (logarithmic) singularity at the Neel temperature. Thereby, we turn to the analysis of the power-law singularity of the phase boundary at $theta=pi$. With $theta-pi$ scaled properly, the $chi_F^{(theta)}$ data are cast into the crossover scaling formula, indicating that the phase boundary is shaped concavely. Such a feature makes a marked contrast to that of the mean-field theory.
We investigate the motion of a colloidal particle driven out of equilibrium by an external torque. We use the molecular dynamics simulation that is alternative to the numerical integration approach based on the Langevin equation and is expected to mimic an experiment more realistically. We choose a heat bath composed of thousands of particles interacting to each other through the Lennard-Jones potential and impose the Langevin thermostat to maintain it in equilibrium. We prepare a single colloidal particle to interact with the particles of the heat bath also by the Lennard-Jones potential while any dissipative force and noise are not employed. We prepare the simulation protocol fit to the overdamped limit in real experiments by increasing the size and mass of the colloidal particle. We study the stochastic properties of the nonequilibrium fluctuations for work and heat produced incessantly in time. We accurately confirm the fluctuation theorem for the work production. We show our results to agree accurately with those from the numerical integration of the Langevin equation.
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