Exploring new frontiers in statistical physics with a new, parallel Wang-Landau framework

Combining traditional Wang-Landau sampling for multiple replica systems with an exchange of densities of states between replicas, we describe a general framework for simulations on massively parallel Petaflop supercomputers. The advantages and general applicability of the method for simulations of complex systems are demonstrated for the classical 2D Potts spin model featuring a strong first-order transition and the self-assembly of lipid bilayers in amphiphilic solutions in a continuous model.

[1]  Harvey Gould,et al.  Overcoming the slowing down of flat-histogram Monte Carlo simulations: cluster updates and optimized broad-histogram ensembles. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Wolfhard Janke,et al.  Microcanonical analyses of peptide aggregation processes. , 2006, Physical review letters.

[3]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[4]  J. Aronovitz,et al.  Universal features of the shapes of percolation clusters and lattice animals , 1987 .

[5]  Kurt Langfeld,et al.  Density of states in gauge theories. , 2012, Physical review letters.

[6]  Nobuyasu Ito,et al.  Evaporation-condensation transition of the two-dimensional Potts model in the microcanonical ensemble. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  D. Landau,et al.  Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  H. R. Warner,et al.  Kinetic Theory and Rheology of Dilute Suspensions of Finitely Extendible Dumbbells , 1972 .

[9]  Raoul Kopelman,et al.  Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm , 1976 .

[10]  D. Landau,et al.  Wang-Landau algorithm for continuous models and joint density of states. , 2005, Physical review letters.

[11]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[12]  R. Baxter.  Potts model at the critical temperature , 1973 .

[13]  D. Landau,et al.  A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling , 2004 .

[14]  Hwee Kuan Lee,et al.  Convergence and refinement of the Wang-Landau algorithm , 2006, Comput. Phys. Commun..

[15]  David P. Landau,et al.  Massively parallel Wang-Landau sampling on multiple GPUs , 2012, Comput. Phys. Commun..

[16]  Juan J. de Pablo,et al.  Monte Carlo simulation of proteins through a random walk in energy space , 2002 .

[17]  Stefan Schnabel,et al.  Microcanonical entropy inflection points: key to systematic understanding of transitions in finite systems. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  David P. Landau,et al.  A new approach to Monte Carlo simulations in statistical physics , 2002 .

[19]  Chiaki Yamaguchi,et al.  Combination of improved multibondic method and the Wang-Landau method. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Wolfhard Janke,et al.  Shape anisotropy of polymers in disordered environment. , 2010, The Journal of chemical physics.

[21]  M. Troyer,et al.  Dynamics of the Wang–Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass , 2004, cond-mat/0405409.

[22]  Chenggang Zhou,et al.  Understanding and improving the Wang-Landau algorithm. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Kurt Binder,et al.  Phase transitions of a single polymer chain: A Wang-Landau simulation study. , 2009, The Journal of chemical physics.

[24]  Thomas Vogel,et al.  Generic, hierarchical framework for massively parallel Wang-Landau sampling. , 2013, Physical review letters.

[25]  Thomas Wüst,et al.  Versatile approach to access the low temperature thermodynamics of lattice polymers and proteins. , 2009, Physical review letters.

[26]  David Chandler,et al.  Mode Expansion in Equilibrium Statistical Mechanics. II. A Rapidly Convergent Theory of Ionic Solutions , 1971 .

[27]  Clare McCabe,et al.  Examining the phase transition behavior of amphiphilic lipids in solution using statistical temperature molecular dynamics and replica-exchange Wang-Landau methods. , 2013, The Journal of chemical physics.

[28]  Takashi Itoh,et al.  Molecular dynamics simulation of amphiphilic molecules in solution: micelle formation and dynamic coexistence. , 2009, The Journal of chemical physics.

[29]  K. Hukushima,et al.  Exchange Monte Carlo Method and Application to Spin Glass Simulations , 1995, cond-mat/9512035.

[30]  Reinhard Lipowsky,et al.  Computer simulations of bilayer membranes - self-assembly and interfacial tension. , 1998 .

[31]  R. Belardinelli,et al.  Fast algorithm to calculate density of states. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  J. Seelig,et al.  The dynamic structure of fatty acyl chains in a phospholipid bilayer measured by deuterium magnetic resonance. , 1974, Biochemistry.