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McNeil-Watson GC, Wilding NB. Freezing line of the Lennard-Jones fluid: A phase switch Monte Carlo study. J Chem Phys 2006; 124:64504. [PMID: 16483217 DOI: 10.1063/1.2166395] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report a phase switch Monte Carlo (PSMC) method study of the freezing line of the Lennard-Jones (LJ) fluid. Our work generalizes to soft potentials the original application of the method to hard-sphere freezing and builds on a previous PSMC study of the LJ system by Errington [J. Chem. Phys. 120, 3130 (2004)]. The latter work is extended by tracing a large section of the Lennard-Jones freezing curve, the results of which we compare with a previous Gibbs-Duhem integration study. Additionally, we provide new background material regarding the statistical-mechanical basis of the PSMC method and extensive implementation details.
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53
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Chen H, Sholl DS. Efficient simulation of binary adsorption isotherms using transition matrix Monte Carlo. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2006; 22:709-16. [PMID: 16401121 DOI: 10.1021/la052373p] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
Molecular simulations of binary adsorption in porous materials are a useful complement to experimental studies of mixture adsorption. Most molecular simulations of binary adsorption are performed using grand canonical Monte Carlo (GCMC) to independently examine a range of state points of interest. A disadvantage of this approach is that it only yields information at a discrete set of state points; therefore, if a complete isotherm is required for arbitrary conditions, some type of data fitting or interpolation must be used in combination with the GCMC data. We show that the transition matrix Monte Carlo (TMMC) method of Shen and Errington (Shen, V. K.; Errington, J. R. J. Chem.Phys. 2005, 122, 064508) is well-suited to simulation of binary adsorption in porous materials. At the completion of a TMMC simulation, the adsorption isotherm for all possible bulk phase compositions and pressures is available without data fitting or interpolation. It is also straightforward to use results from TMMC to compute derivatives of the isotherm such as the mixture thermodynamic correction factors, partial differential ln f(i)/partial differential ln c(j), again without data fitting or interpolation. This approach should be useful in contexts where information on the full adsorption isotherm is needed, such as the design of adsorption- or membrane-based separations.
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Affiliation(s)
- Haibin Chen
- Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
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54
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Shen VK, Errington JR. Determination of surface tension in binary mixtures using transition-matrix Monte Carlo. J Chem Phys 2006; 124:024721. [PMID: 16422640 DOI: 10.1063/1.2159472] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We present a methodology based on grand-canonical transition-matrix Monte Carlo and finite-size scaling analysis to calculate surface tensions in binary mixtures. In particular, mixture transition-matrix Monte Carlo is first used to calculate apparent, system-size-dependent free-energy barriers separating coexisting fluid phases. Finite-size scaling is then used to extrapolate these values to the infinitely large system limit to determine the true thermodynamic surface tension. A key distinction of the methodology is that it yields the entire isothermal surface-tension curve for a binary mixture in a relatively small number of simulations. We demonstrate the utility of the method by calculating surface-tension curves for three binary Lennard-Jones mixtures. While we have only examined the surface tension of simple fluids in this work, the method is general and can be extended to molecular fluids as well as to determine interfacial tensions of liquid-liquid interfaces.
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Affiliation(s)
- Vincent K Shen
- Physical and Chemical Properties Division, National Institute of Standards and Technology, 100 Bureau Drive MS 8380, Gaithersburg, Maryland 20899-8380, USA.
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55
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Shell MS, Debenedetti PG, Panagiotopoulos AZ. Computational characterization of the sequence landscape in simple protein alphabets. Proteins 2005; 62:232-43. [PMID: 16284961 DOI: 10.1002/prot.20714] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
We characterize the "sequence landscapes" in several simple, heteropolymer models of proteins by examining their mutation properties. Using an efficient flat-histogram Monte Carlo search method, our approach involves determining the distribution in energy of all sequences of a given length when threaded through a common backbone. These calculations are performed for a number of Protein Data Bank structures using two variants of the 20-letter contact potential developed by Miyazawa and Jernigan [Miyazawa S, Jernigan WL. Macromolecules 1985;18:534], and the 2-monomer HP model of Lau and Dill [Lau KF, Dill KA. Macromolecules 1989;22:3986]. Our results indicate significant differences among the energy functions in terms of the "smoothness" of their landscapes. In particular, one of the Miyazawa-Jernigan contact potentials reveals unusual cooperative behavior among its species' interactions, resulting in what is essentially a set of phase transitions in sequence space. Our calculations suggest that model-specific features can have a profound effect on protein design algorithms, and our methods offer a number of ways by which sequence landscapes can be quantified.
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Affiliation(s)
- M Scott Shell
- Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA.
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56
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Gospodinov ID, Escobedo * FA. Probability density of macrostates and density of states for multi-component mixtures from semi-empirical equations of state. Mol Phys 2005. [DOI: 10.1080/00268970500243812] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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57
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Reynal S, Diep HT. Fast flat-histogram method for generalized spin models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:056710. [PMID: 16383788 DOI: 10.1103/physreve.72.056710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2005] [Revised: 10/03/2005] [Indexed: 05/05/2023]
Abstract
We present a Monte Carlo method that efficiently computes the density of states for spin models having any number of interaction per spin. By combining a random walk in the energy space with collective updates controlled by the microcanonical temperature, our method yields dynamic exponents close to their ideal random-walk values, reduced equilibrium times, and very low statistical error in the density of states. The method can host any density of states estimation scheme, including the Wang-Landau algorithm and the transition matrix method. Our approach proves remarkably powerful in the numerical study of models governed by long-range interactions, where it is shown to reduce the algorithm complexity to that of a short-range model with the same number of spins. We apply the method to the -state Potts chains with power-law decaying interactions in their first-order regime; we find that conventional local-update algorithms are outperformed already for sizes above a few hundred spins. By considering chains containing up to spins, which we simulated in fairly reasonable time, we obtain estimates of transition temperatures correct to five-figure accuracy. Finally, we propose several efficient schemes aimed at estimating the microcanonical temperature.
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Affiliation(s)
- S Reynal
- Laboratoire de Physique Théorique et Modélisation, CNRS-Université de Cergy-Pontoise (UMR 8089), 2 avenue A. Chauvin, F-95302 Cergy-Pontoise Cedex, France.
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58
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Errington JR, Shen VK. Direct evaluation of multicomponent phase equilibria using flat-histogram methods. J Chem Phys 2005; 123:164103. [PMID: 16268677 DOI: 10.1063/1.2064628] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a method for directly locating density-driven phase transitions in multicomponent systems. Phase coexistence conditions are determined through manipulation of a total density probability distribution evaluated over a density range that includes both coexisting phases. Saturation quantities are determined through appropriate averaging of density-dependent mean values of a given property of interest. We discuss how to implement the method in both the grand-canonical and isothermal-isobaric semigrand ensembles. Calculations can be conducted using any of the recently introduced flat-histogram techniques. Here, we combine the general algorithm with a transition-matrix approach to produce an efficient self-adaptive technique for determining multicomponent phase equilibrium properties. To assess the performance of the new method, we generate phase diagrams for a number of binary and ternary Lennard-Jones mixtures.
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Affiliation(s)
- Jeffrey R Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
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59
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Gospodinov ID, Escobedo FA. Multicanonical schemes for mapping out free-energy landscapes of single-component and multicomponent systems. J Chem Phys 2005; 122:164103. [PMID: 15945668 DOI: 10.1063/1.1884594] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023] Open
Abstract
Multicanonical (MUCA) sampling is a powerful approach for simulating large domains of thermodynamic macrostate space that relies on mapping out either the density of states or a free energy of the system as a function of a suitable "order parameter." The purpose of this study is to extend and apply to more complex systems the method introduced in a previous paper [M. K. Fenwick and F. A. Escobedo, J. Chem. Phys. 120, 3066 (2004)] that uses Bennett's acceptance ratio method for estimating MUCA free energies. Four types of MUCA schemes are considered according to what order parameter is adopted and how the macrostate space is traversed: a la grand canonical ensemble, a la semigrand canonical ensemble, a la semigrand isothermal-isobaric ensemble, and a la isothermal-isobaric ensemble. Two types of systems are studied, the first is a two-component Lennard-Jones mixture that exhibits a vapor-liquid transition, and the second is a hard-cuboid containing system that exhibits an isotropic-liquid crystalline transition. These systems are simulated with different MUCA schemes and the resulting free-energy profiles are used to determine phase-coexistence conditions. For the Lennard-Jones systems, it is also demonstrated that different types of MUCA simulations can be conveniently performed over different macrostate regions and the results can be subsequently pieced together into a continuous weighting function.
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Affiliation(s)
- Ivan D Gospodinov
- School of Chemical & Biomolecular Engineering, Cornell University, Ithaca, New York 14853-5201, USA
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60
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Shen VK, Errington JR. Determination of fluid-phase behavior using transition-matrix Monte Carlo: Binary Lennard-Jones mixtures. J Chem Phys 2005; 122:064508. [PMID: 15740389 DOI: 10.1063/1.1844372] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
We present a novel computational methodology for determining fluid-phase equilibria in binary mixtures. The method is based on a combination of highly efficient transition-matrix Monte Carlo and histogram reweighting. In particular, a directed grand-canonical transition-matrix Monte Carlo scheme is used to calculate the particle-number probability distribution, after which histogram reweighting is used as a postprocessing procedure to determine the conditions of phase equilibria. To validate the methodology, we have applied it to a number of model binary Lennard-Jones systems known to exhibit nontrivial fluid-phase behavior. Although we have focused on monatomic fluids in this work, the method presented here is general and can be easily extended to more complex molecular fluids. Finally, an important feature of this method is the capability to predict the entire fluid-phase diagram of a binary mixture at fixed temperature in a single simulation.
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Affiliation(s)
- Vincent K Shen
- National Institute of Standards and Technology, Physical and Chemical Properties Division, Gaithersburg, Maryland 20899-8380, USA.
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61
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Earl DJ, Deem MW. Markov Chains of Infinite Order and Asymptotic Satisfaction of Balance: Application to the Adaptive Integration Method. J Phys Chem B 2005; 109:6701-4. [PMID: 16851753 DOI: 10.1021/jp045508t] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.
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Affiliation(s)
- David J Earl
- Departments of Bioengineering and Physics & Astronomy, Rice University, 6100 Main Street-MS 142, Houston, Texas 77005-1892, USA
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62
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Shell MS, Debenedetti PG, Panagiotopoulos AZ. Flat-Histogram Dynamics and Optimization in Density of States Simulations of Fluids. J Phys Chem B 2004. [DOI: 10.1021/jp047677j] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- M. Scott Shell
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544
| | - Pablo G. Debenedetti
- Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544
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63
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Magee JE, Warwicker J, Lue L. Freezing and folding behavior in simple off-lattice heteropolymers. J Chem Phys 2004; 120:11285-91. [PMID: 15268156 DOI: 10.1063/1.1740750] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We have performed parallel tempering Monte Carlo simulations using a simple continuum heteropolymer model for proteins. All 10 heteropolymer sequences which we have studied have shown first-order transitions at low temperature to ordered states dominated by single chain conformations. These results are in contrast with the theoretical predictions of the random energy model for heteropolymers, from which we would expect continuous transitions to glassy behavior at low temperatures.
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Affiliation(s)
- J E Magee
- Department of Chemical Engineering, UMIST, PO Box 88, Manchester, M60 1QD, United Kingdom.
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64
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Virnau P, Muller M. Calculation of free energy through successive umbrella sampling. J Chem Phys 2004; 120:10925-30. [PMID: 15268122 DOI: 10.1063/1.1739216] [Citation(s) in RCA: 201] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider an implementation of umbrella sampling in which the pertinent range of states is subdivided into small windows that are sampled consecutively and linked together. This allows us to simulate without a weight function or to extrapolate the results to the neighboring window in order to estimate a weight function. Additionally, we present a detailed error analysis in which we demonstrate that the error in umbrella sampling is controlled and, in the absence of sampling difficulties, independent of the window sizes. In this case, the efficiency of our implementation is comparable to a multicanonical simulation with a very good weight function, which in our scheme does not need to be known ahead of time. The analysis also allows us to detect sampling difficulties such as correlations between adjacent windows and provides a test of equilibration. We exemplify the scheme by simulating the liquid-vapor coexistence in a Lennard-Jones system.
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Affiliation(s)
- Peter Virnau
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA.
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65
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Fasnacht M, Swendsen RH, Rosenberg JM. Adaptive integration method for Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056704. [PMID: 15244974 DOI: 10.1103/physreve.69.056704] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2003] [Indexed: 05/24/2023]
Abstract
We present an adaptive sampling method for computing free energies, radial distribution functions, and potentials of mean force. The method is characterized by simplicity and accuracy, with the added advantage that the data are obtained in terms of quasicontinuous functions. The method is illustrated and tested with simulations on a high density fluid, including a stringent consistency test involving an unusual thermodynamic cycle that highlights its advantages.
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Affiliation(s)
- Marc Fasnacht
- Physics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA.
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66
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Errington JR. Prewetting transitions for a model argon on solid carbon dioxide system. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2004; 20:3798-804. [PMID: 15875418 DOI: 10.1021/la0360106] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
Grand canonical transition matrix Monte Carlo simulations are used to investigate the phase behavior of the model argon on solid carbon dioxide system introduced by Ebner and Saam (Phys. Rev. Lett. 1977, 38, 1486). Our results indicate that the system exhibits first-order prewetting transitions at temperatures above a wetting temperature of Tw = 0.598(5) and below a critical prewetting temperature of Tpwc approximately 0.92. The wetting transition is identified by determining the temperature at which the difference between the bulk vapor-liquid and prewetting saturation chemical potentials goes to zero. Coexistence is directly located at a given temperature by obtaining a density probability distribution from simulation data and utilizing histogram reweighting to determine the conditions that satisfy phase coexistence. Structural properties of the adsorbed films are also examined.
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Affiliation(s)
- Jeffrey R Errington
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA.
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67
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Errington JR. Solid–liquid phase coexistence of the Lennard-Jones system through phase-switch Monte Carlo simulation. J Chem Phys 2004; 120:3130-41. [PMID: 15268465 DOI: 10.1063/1.1642591] [Citation(s) in RCA: 66] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The phase-switch Monte Carlo method of Wilding and Bruce [Phys. Rev. Lett. 85, 5138 (2000)] is extended to enable calculation of solid-liquid phase coexistence for soft potentials. The method directly accesses coexistence information about a system while avoiding simulation of the interfacial region. Order parameters are introduced that allow one to define a path that connects liquid and crystalline phases. Transition matrix methods are employed to bias the sampling such that both phases are sampled in a rapid and efficient manner. Coexistence properties are determined through an analysis of specific volume probability distributions, which are generated naturally during a biased simulation. The approach is demonstrated with the Lennard-Jones system. Finite-size effects are examined and compared to those for the hard sphere system. In addition, two techniques are considered for accounting for long-range interactions. The methodology presented here is general and therefore provides a basis for its application to other soft systems.
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Affiliation(s)
- Jeffrey R Errington
- Department of Chemical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA.
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68
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Hilfer R, Biswal B, Mattutis HG, Janke W. Multicanonical Monte Carlo study and analysis of tails for the order-parameter distribution of the two-dimensional Ising model. ACTA ACUST UNITED AC 2003; 68:046123. [PMID: 14683018 DOI: 10.1103/physreve.68.046123] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2003] [Indexed: 11/07/2022]
Abstract
The tails of the critical order-parameter distribution of the two-dimensional Ising model are investigated through extensive multicanonical Monte Carlo simulations. Results for fixed boundary conditions are reported here, and compared with known results for periodic boundary conditions. Clear numerical evidence for "fat" stretched exponential tails exists below the critical temperature, indicating the possible presence of fat tails at the critical temperature. Our work suggests that the true order-parameter distribution at the critical temperature must be considered to be unknown at present.
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Affiliation(s)
- R Hilfer
- ICA-1, Universität Stuttgart, Pfaffenwaldring 27, 70569 Stuttgart, Germany
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69
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Fenwick MK, Escobedo FA. Expanded ensemble and replica exchange methods for simulation of protein-like systems. J Chem Phys 2003. [DOI: 10.1063/1.1624822] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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70
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Shell MS, Debenedetti PG, Panagiotopoulos AZ. An improved Monte Carlo method for direct calculation of the density of states. J Chem Phys 2003. [DOI: 10.1063/1.1615966] [Citation(s) in RCA: 121] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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71
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Errington JR. Direct calculation of liquid–vapor phase equilibria from transition matrix Monte Carlo simulation. J Chem Phys 2003. [DOI: 10.1063/1.1572463] [Citation(s) in RCA: 241] [Impact Index Per Article: 11.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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72
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Errington JR. Evaluating surface tension using grand-canonical transition-matrix Monte Carlo simulation and finite-size scaling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:012102. [PMID: 12636539 DOI: 10.1103/physreve.67.012102] [Citation(s) in RCA: 123] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2002] [Indexed: 05/24/2023]
Abstract
This Brief Report describes an approach for determining the surface tension of a model system that is applicable over the entire liquid-vapor coexistence region. At the heart of the method is a technique for determining coexistence properties that utilize transition probabilities of attempted Monte Carlo moves during a grand canonical simulation. Finite-size scaling techniques are implemented to determine the infinite system surface tension from a series of finite-size simulations. To demonstrate the method, the surface tension of the Lennard-Jones fluid is determined at temperatures ranging from the triple point to the critical point.
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Affiliation(s)
- Jeffrey R Errington
- Department of Chemical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
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73
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Jackson AN, Bruce AD, Ackland GJ. Lattice-switch Monte Carlo method: application to soft potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:036710. [PMID: 11909310 DOI: 10.1103/physreve.65.036710] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2001] [Indexed: 05/23/2023]
Abstract
The lattice-switch Monte Carlo method, recently introduced and applied in the context of hard spheres, is extended to particles interacting through a soft potential. The method utilizes a transformation that switches between configurations of two different crystalline structures, allowing the phase space of both structures to be explored in a single simulation and the difference between their free energies to be determined directly. We apply the method to determine the fcc-hcp crystalline phase behavior of the classical Lennard-Jones solid.
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Affiliation(s)
- A N Jackson
- Department of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland, United Kingdom
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74
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Kastner M, Promberger M, Munoz JD. Broad histogram method: extension and efficiency test. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:7422-9. [PMID: 11102104 DOI: 10.1103/physreve.62.7422] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/1999] [Revised: 01/25/2000] [Indexed: 11/07/2022]
Abstract
Compared to standard histogram techniques, the broad histogram method allows us to increase the efficiency of Monte Carlo simulations by a tremendous amount. This gain of efficiency is achieved by measuring simulation averages of particular system observables (different from those used in standard histogram techniques), while the algorithm of the simulation can be left unchanged. In this paper, the broad histogram method is reformulated in a more mathematical and precise way. Furthermore, the method is extended to estimate the density of states as a function of more than one parameter. A quantitative investigation of the gain of efficiency of Monte Carlo simulations is performed. For the broad histogram method, we find a gain of efficiency which amounts to orders of magnitude in comparison to the standard histogram method.
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Affiliation(s)
- M Kastner
- Institut fur Theoretische Physik, Universitat Erlangen-Nurnberg, Staudtstrasse 7, 91058 Erlangen, Germany
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Bruce AD, Jackson AN, Ackland GJ, Wilding NB. Lattice-switch monte carlo method. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:906-19. [PMID: 11046340 DOI: 10.1103/physreve.61.906] [Citation(s) in RCA: 55] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/1999] [Indexed: 11/07/2022]
Abstract
We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by "switching" one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to gateway arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.
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Affiliation(s)
- AD Bruce
- Department of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland, United Kingdom
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77
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Bruce AD, Wilding NB. Critical-point finite-size scaling in the microcanonical ensemble. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3748-60. [PMID: 11970208 DOI: 10.1103/physreve.60.3748] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/1999] [Indexed: 04/18/2023]
Abstract
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.
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Affiliation(s)
- A D Bruce
- Department of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland, United Kingdom
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78
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Lyubartsev AP, Fo/rrisdahl OK, Laaksonen A. Solvation free energies of methane and alkali halide ion pairs: An expanded ensemble molecular dynamics simulation study. J Chem Phys 1998. [DOI: 10.1063/1.475374] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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