Abstract: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 magnetiza… Show more
“…The general source of these difficulties seems to be due to the difficulty in matching surfaces at the boundaries rather than curves as in one-dimensional random walks [44]. To overcome this problem, Cunha-Netto et al proposed the WLS with adaptive windows [45],…”
The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic nearest-neighbor interactions (J 1 ) and antiferromagnetic next-nearest-neighbor couplings (J 2 ) are analyzed in the plane temperature versus α, where α = J 2 /|J 1 | is the frustration parameter.We used the original Wang-Landau sampling and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature reentrant behavior, observed in the frontier separating the ferromagnetic and the colinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo simulations of the model. In addition, our results indicate that the continuous phase transition between the Ferromagnetic and the Paramagnetic phases, that occurs for 0.0 ≤ α < 0.25, belongs to the universality class of the three-dimensional pure Ising Model.
“…The general source of these difficulties seems to be due to the difficulty in matching surfaces at the boundaries rather than curves as in one-dimensional random walks [44]. To overcome this problem, Cunha-Netto et al proposed the WLS with adaptive windows [45],…”
The qualitative aspects of the phase diagram of the Ising model on the cubic lattice, with ferromagnetic nearest-neighbor interactions (J 1 ) and antiferromagnetic next-nearest-neighbor couplings (J 2 ) are analyzed in the plane temperature versus α, where α = J 2 /|J 1 | is the frustration parameter.We used the original Wang-Landau sampling and the standard Metropolis algorithm to confront past results of this model obtained by the effective-field theory (EFT) for the cubic lattice. Our numerical results suggest that the predictions of the EFT are in general qualitatively correct, but the low-temperature reentrant behavior, observed in the frontier separating the ferromagnetic and the colinear order, is an artifact of the EFT approach and should disappear when we consider Monte Carlo simulations of the model. In addition, our results indicate that the continuous phase transition between the Ferromagnetic and the Paramagnetic phases, that occurs for 0.0 ≤ α < 0.25, belongs to the universality class of the three-dimensional pure Ising Model.
“…The algorithm of a random walk to extract the JDOS is better known for calculations of thermal averages. [19][20][21][22][23][24][25][26] Apparently the JDOS algorithm for ͑r , E͒ variables is a promising tool for calculations of the thermodynamics of conformational changes as well. 25 The JDOS algorithm is a straightforward extension of the original Wang-Landau ͑WL͒ sampling algorithm.…”
A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.
“…This is because, in semi-grand-canonical ensemble for multicomponent alloys, a multi-dimensional DOS is typically required. The WL studies on a multidimensional density of states [12][13][14][15][16][17] shows some difficulties such as the connecting the pieces of W (E) and computational costs. Although the difficulties has been overcome by such as the multi-parallel framework [14][15][16][17] , constructing a multi-dimensional density of states remains quite a difficult problem.…”
We develop an approach to apply Wang-Landau algorithm to multicomponent alloys in semigrand-canonical ensemble. Although the Wang-Landau algorithm has great advantages over conventional sampling methods, there are few applications to alloys. This is because calculating compositions in semi-grand-canonical ensemble using the Wang-Landau algorithm requires a multidimensional density of states in terms of total energy and compositions. However, constructing the multi-dimensional density of states is difficult. In this study, we develop a simple approach to calculate the alloy phase diagram using Wang-Landau algorithm, and show that compositions in semi-grand-canonical ensemble require just some one-dimensional densities of states. Finally, we applied the present method to Cu-Au and Pd-Rh alloys and confirmed that the present method successfully describes the phase diagram with high validity and accuracy.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.