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Monte Carlo algorithms can provide detailed information about the static properties of magnets and spin dynamics simulations can be used to understand their dynamic properties. We present an introduction to these methods and discuss some simple examples, showing the insights that can be gained. [DOI: 10.1119/1.2839563]

Decomposition algorithms have proven useful for molecular dynamics and spin dynamics simulations of many-body systems. These methods are time reversible, symplectic, and the error in the total energy is bounded. In general, these techniques are accurate for much larger time steps than more standard integration methods. We review these decomposition algorithms and illustrate their performance for simulations of a Heisenberg ferromagnet. [DOI: 10.1119/1.1900096]

(Received 15 December 2003; accepted 20 February 2004) We describe a Monte Carlo algorithm for doing simulations in classical statistical physics in a different way. Instead of sampling the probability distribution at a fixed temperature, a random walk is performed in energy space to extract an estimate for the density of states. The probability can be computed at any temperature by weighting the density of states by the appropriate Boltzmann factor. Thermodynamic properties can be determined from suitable derivatives of the partition function and, unlike 'standard' methods, the free energy and entropy can also be computed directly. To demonstrate the simplicity and power of the algorithm, we apply it to models exhibiting first-order or second-order phase transitions. [DOI: 10.1119/1.1707017]

Monte Carlo simulations are reported to analyze the effect of the ferromagnetic on the transition between disordered and ordered states in the antiferromagnetic for various film thickness and compensated exchange across the ferromagnetic-antiferromagnetic interface. The preliminary simulations suggest that both phase transition temperatures increase with the film thickness.

Monte Carlo simulations have been used to study magnetic ordering in coupled anisotropic ferro/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. We consider films with flat interfaces that are fully uncompensated as well as rough interfaces that are compensated on average. For both types of interfaces above the "Néel temperature" we observed order in the AFM with the AFM spins aligning collinearly with the FM moments. In the case of rough interfaces there is a transition from collinear to perpendicular alignment of the FM and AFM spins at a lower temperature. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations and ground-state calculations have been used to map out the phase diagram of a system of classical spins, on a simple cubic lattice, where nearest-neighbor pairs of spins are coupled via competing antiferromagnetic superexchange and ferromagnetic double-exchange interactions. For a certain range of parameters, this model is relevant for some magnetic materials, such as doped manganites, which exhibit the remarkable colossal magnetoresistance effect. The phase diagram includes two regions in which the two sublattice magnetizations differ in magnitude. Spin-dynamics simulations have been used to compute the time- and space-displaced spin–spin correlation functions, and their Fourier transforms, which yield the dynamic structure factor S(q,ω) for this system. Effects of the double-exchange interaction on the dispersion curves are shown. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Lots of lithium ion battery (LIB) products contain lithium metal oxide LiNi5Co2Mn3O2 (LNCM) as the positive electrode's active material. The stable surface of this oxide results in high resistivity in the battery. For this reason, conductive carbon-based materials, including acetylene black and carbon black, become necessary components in electrodes. Recently, carbon nano-tube (CNT) has appeared as a popular choice for the conductive carbon in LIB. However, a large quantity of the conductive carbon, which cannot provide capacity as the active material, will decrease the energy density of batteries. The ultra-high cost of CNT, compared to conventional carbon black, is also a problem. In this work, we are going to introduce long-length carbon nano-tube s(L-CNT) into electrodes in order to design a reduced-amount conductive carbon electrode. The whole experiment will be done in a 1Ah commercial type pouch LIB. By decreasing conductive carbon as well as increasing the active material in the positive electrode, the energy density of the LNCM-based 1Ah pouch type LIB, with only 0.16% of L-CNT inside the LNCM positive electrode, could reach 224 Wh/kg and 549 Wh/L, in weight and volume energy density, respectively. Further, this high energy density LIB with L-CNT offers stable cyclability, which may constitute valuable progress in portable devices and electric vehicle (EV) applications. [ABSTRACT FROM AUTHOR]

Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a L×L×L simple cubic lattice for the first-order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension L the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor q that characterizes the relative degeneracy of the ordered phases. Our theory yields q=π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first-order phase transitions.

We use Monte Carlo simulations to study the XXZ Heisenberg antiferromagnet in a field in order to clearly determine the nature of the multicritical point. We use a hybrid sampling method with Metropolis and Wolff-cluster algorithms, along with histogram reweighting techniques. Staggered magnetization susceptibilities, Binder cumulants, and finite-size scaling are considered in an effort to detect a possible biconical phase. An analysis of the probability distribution of the magnetization allowed us to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) is shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.

We present extensive Monte Carlo spin-dynamics simulations of the vector Blume-Emery-Griffiths model with three-dimensional spins on a simple cubic lattice and periodic boundary conditions. For a range of Hamiltonian parameters, this model reproduces the phase diagram topology of the one experimentally observed for bulk mixtures of 3He-4He . Highly efficient decomposition time integration algorithms have been used to obtain the evolution of the equations of motion from which we have computed the dynamic structure factor S(q,omega) close to critical and tricritical points. The dispersion relation and the corresponding dynamic exponents have been obtained in the critical and multicritical transitions. We find that the dynamic critical exponents for in-plane and out-of-plane fluctuations are the same at the tricritical point but are in fact different along the critical line.

Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.