Shan-Ho Tsai

Improving Wang-Landau sampling with adaptive windows.

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.

Uncovering the secrets of unusual phase diagrams: applications of two-dimensional Wang-Landau sampling

We use a two-dimensional Wang-Landau sampling algorithm to calculate the density of states for two discrete spin models and then extract their phase diagrams. The first system is an asymmetric Ising model on a triangular lattice with two- and three-body interactions in an external field. An accurate density of states allows us to locate the critical endpoint accurately in a two-dimensional parameter space. We observe a divergence of the spectator phase boundary and of the temperature derivative of the magnetization coexistence diameter at the critical endpoint in quantitative agreement with theoretical predictions. The second model is a Q-state Potts model in an external field H. We map the phase diagram of this model for Q > 8 and observe a first-order phase transition line that starts at the H = 0 phase transition point and ends at a critical point (Tc,Hc), which must be located in a two-dimensional parameter space. The critical field Hc(Q) is positive and increases with Q, in qualitative agreement with previous theoretical predictions.

Phase diagram of a two-dimensional large-Q Potts model in an external field

Abstract We use a two-dimensional Wang–Landau sampling algorithm to map out the phase diagram of a Q-state Potts model with Q ⩽ 10 in an external field H that couples to one state. Finite-size scaling analyses show that for large Q the first-order phase transition point at H = 0 is in fact a triple point at which three first-order phase transition lines meet. One such line is restricted to H = 0 ; another line has H ⩽ 0 . The third line, which starts at the H = 0 triple point, ends at a critical point ( T c , H c ) which needs to be located in a two-dimensional parameter space. The critical field H c ( Q ) is positive and decreases with decreasing Q, which is in qualitative agreement with previous predictions.

Critical endpoint behavior : A Wang-Landau study

Abstract We study the critical endpoint behavior using an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. The simulation method we use is Wang–Landau sampling in a two-dimensional parameter space. 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.

Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this difficulty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.

Two-Dimensional Wang–Landau Sampling Of An Asymmetric Ising Model

We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang–Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

Bicritical or tetracritical: the 3D anisotropic Heisenberg antiferromagnet

The classical uniaxially anisotropic Heisenberg antiferromagnet on the simple cubic lattice, in the presence of an external magnetic field, is believed to have a multicritical point; however, there has been controversy whether it is a bicritical or a tetracritical point. We perform Monte Carlo simulations of this model and analyze the components of the staggered magnetization, the susceptibilities and the probability distribution of the magnetization to conclude that the multicritical point is bicritical and it is in the three-dimensional Heisenberg universality class.

Spin Dynamics: An Atomistic Simulation Tool for Magnetic Systems

Spin dynamics methods can provide insight into excitations and dynamic critical behavior of magnetic systems and can now enable the study of such systems with a precision that equals or exceeds that of experiment.