Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWang-Landau algorithm for continuous models and joint density of states
155
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states $g(M,E)$ of ferromagnet Heisenberg models. The joint density of states contains more information than the density of states of a single variable--energy, but is also much more time-consuming to calculate. We discuss the strategies to perform this calculation efficiently for models with several thousand degrees of freedom, much larger than other continuous models studied previously with the Wang-Landau algorithm.
rate research
Read More
We propose a strategy to achieve the fastest convergence in the Wang-Landau algorithm with varying modification factors. With this strategy, the convergence of a simulation is at least as good as the conventional Monte Carlo algorithm, i.e. the statistical error vanishes as $1/sqrt{t}$, where $t$ is a normalized time of the simulation. However, we also prove that the error cannot vanish faster than $1/t$. Our findings are consistent with the $1/t$ Wang-Landau algorithm discovered recently, and we argue that one needs external information in the simulation to beat the conventional Monte Carlo algorithm.
We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the mixing time of the Markov chain. We estimate numerically the dependence of the mixing time on the lattice size, and extract the mixing exponent.
Monte Carlo simulations using the newly proposed Wang-Landau algorithm together with the broad histogram relation are performed to study the antiferromagnetic six-state clock model on the triangular lattice, which is fully frustrated. We confirm the existence of the magnetic ordering belonging to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral ordering which occurs at slightly higher temperature. We also observe the lower temperature phase transition of KT type due to the discrete symmetry of the clock model. By using finite-size scaling analysis, the higher KT temperature $T_2$ and the chiral critical temperature $T_c$ are respectively estimated as $T_2=0.5154(8)$ and $T_c=0.5194(4)$. The results are in favor of the double transition scenario. The lower KT temperature is estimated as $T_1=0.496(2)$. Two decay exponents of KT transitions corresponding to higher and lower temperatures are respectively estimated as $eta_2=0.25(1)$ and $eta_1=0.13(1)$, which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.
The Wang-Landau method is used to study the magnetic properties of the giant paramagnetic molecule Mo_72Fe_30 in which 30 Fe3+ ions are coupled via antiferromagnetic exchange. The two-dimensional density of states g(E,M) in energy and magnetization space is calculated using a self-adaptive version of the Wang-Landau method. From g(E,M) the magnetization and magnetic susceptibility can be calculated for any temperature and external field.
By combining two generalized-ensemble algorithms, Replica-Exchange Wang-Landau (REWL) method and Multicanonical Replica-Exchange Method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed next. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model by the three methods, namely, REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by the REWL-MUCAREM is more accurate than that is estimated by the two methods separately.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
