Accelerated spin dynamics using deep learning corrections.

Theoretical models capture very precisely the behaviour of magnetic materials at the microscopic level. This makes computer simulations of magnetic materials, such as spin dynamics simulations, accurately mimic experimental results. New approaches to efficient spin dynamics simulations are limited by integration time step barrier to solving the equations-of-motions of many-body problems. Using a short time step leads to an accurate but inefficient simulation regime whereas using a large time step leads to accumulation of numerical errors that render the whole simulation useless. In this paper, we use a Deep Learning method to compute the numerical errors of each large time step and use these computed errors to make corrections to achieve higher accuracy in our spin dynamics. We validate our method on the 3D Ferromagnetic Heisenberg cubic lattice over a range of temperatures. Here we show that the Deep Learning method can accelerate the simulation speed by 10 times while maintaining simulation accuracy and overcome the limitations of requiring small time steps in spin dynamic simulations.

First-order phase transition and tricritical scaling behavior of the Blume-Capel model: A Wang-Landau sampling approach.

We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the Wang-Landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first Wang-Landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.

Scaling exponents and transition behavior of the generalized conserved lattice gas model at zero temperature.

We study a generalized conserved lattice gas model in two dimensions by introducing an effective temperature to the conserved lattice gas model, where the number of particles is conserved during the dynamical process. We apply Monte Carlo simulation with the Metropolis transition rate. At zero temperature we find two transition behaviors; one between the localized active states and absorbing states and the other between the localized active states and active states. With a different definition of the order parameter for the second transition behavior, we obtain the critical exponents at the transition point.

Existence of an upper critical dimension in the majority voter model.

We study the critical properties of the majority voter model on d -dimensional hypercubic lattices. In two dimensions, the majority voter model belongs to the same universality class as that of the Ising model. However, the critical behaviors of the majority voter model on four dimensions do not exhibit mean-field behavior. Using the Monte Carlo simulation on d -dimensional hypercubic lattices, we obtain the critical exponents up to d=7 , and find that the upper critical dimension is 6 for the majority voter model. We also confirm our results using mean-field calculation.

Three-dimensional non-destructive optical evaluation of laser-processing performance using optical coherence tomography.

We demonstrate the use of optical coherence tomography (OCT) as a non-destructive diagnostic tool for evaluating laser-processing performance by imaging the features of a pit and a rim. A pit formed on a material at different laser-processing conditions is imaged using both a conventional scanning electron microscope (SEM) and OCT. Then using corresponding images, the geometrical characteristics of the pit are analyzed and compared. From the results, we could verify the feasibility and the potential of the application of OCT to the monitoring of the laser-processing performance.

Critical behavior of the majority voter model is independent of transition rates.

We study the critical properties of the majority voter model by using two different transition rates: the Glauber rate and the Metropolis rate. The model with the Glauber rate has been found to be mapped to the majority voter model with noise [de Oliveira, J. Stat. Phys. 66, 273 (1992)]. The critical temperature and the critical exponents for the two transition rates are obtained from a Monte Carlo simulation with a finite size scaling analysis. The critical temperature is found to depend on the transition rate, but the critical exponents do not. The values of the critical exponents obtained indicate that the model belongs to the same universality class as the Ising model, regardless of the type of transition rate.

Critical behavior of the XY model on growing scale-free networks.

Applying the histogram reweighting method, we investigate the critical behavior of the XY model on growing scale-free networks with various degree exponents lambda. For lambda < or = 3 , the critical temperature diverges as it does for the Ising model on scale-free networks. For lambda=8 , on the other hand, we observe a second-order phase transition at finite temperature. We obtain the critical temperature T{c}=3.08(2) and the critical exponents nu=2.62(3) , gammanu=0.127(4) , and betanu=0.442(2) from a finite-size scaling analysis.

Sub-block order parameter in a driven Ising lattice gas using block distribution functions.

We investigate the order parameter of the standard Ising lattice gas and driven Ising lattice gas models. The sub-block order parameter is introduced to these conserved models as an order parameter using block distribution functions. We also introduce the sub-block order parameter of damage using the block distribution functions of damage. We measure the sub-block order parameters using the Metropolis and heat-bath rates. These order parameters work well for the non-equilibrium-conserved model as well as the equilibrium-conserved model. We obtain the critical exponent of order parameter beta=1/8 for the standard Ising lattice gas and beta=1/2 for a driven Ising lattice gas using the Metropolis and heat-bath rates.

Efficient sampling of protein structures by model hopping.

We introduce a novel simulation method, model hopping, that enhances sampling of low-energy configurations in complex systems. The approach is illustrated for a protein-folding problem. Thermodynamic quantities of proteins with up to 46 residues are evaluated from all-atom simulations with this method.

Driven diffusive systems: how steady states depend on dynamics.

In contrast to equilibrium systems, nonequilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber, and heat bath rates, we illustrate this expectation for an Ising lattice gas, driven far from equilibrium by an "electric" field. While heat bath and Glauber rates generate essentially identical data for structure factors and two-point correlations, Metropolis rates give noticeably weaker correlations, as if the "effective" temperature were higher in the latter case. We also measure energy histograms and define a simple ratio which is exactly known and closely related to the Boltzmann factor for the equilibrium case. For the driven system, the ratio probes a thermodynamic derivative which is found to be dependent on dynamics.