Abstract The Weighted Histogram Analysis Method (WHAM), an extension of Ferrenberg and Swendsen's Multiple Technique, has been applied for the first time on complex biomolecular Hamiltonians. method is presented here as Umbrella Sampling free‐energy Potential Mean Force calculations. This algorithm possesses following advantages over methods that are currently employed: (1) It provides a built‐in estimate sampling errors thereby yielding objective estimates optimal location length additional...

A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality. The algorithm violates dynamic universality at second-order phase transitions, producing unusually small values the dynamical critical exponent.

We present a new method for using the data from Monte Carlo simulations that can increase efficiency by 2 or more orders of magnitude. A single simulation is sufficient to obtain complete thermodynamic information over entire scaling region near phase transition. The accuracy demonstrated comparison with exact results d=2 Ising model. New eight-state Potts model are also presented. generally applicable statistical models and lattice-gauge theories.

We present a new method for optimizing the analysis of data from multiple Monte Carlo computer simulations over wide ranges parameter values. Explicit error estimates allow objective planning lengths runs and values to be simulated. The is applicable in lattice gauge theories, chemistry, biology, as well statistical mechanics.

A new Monte Carlo method is presented for simulations of systems with quenched random interactions. The approach greatly reduces the long correlation times characteristic standard methods, allowing investigation lower temperatures less computer time than previously necessary.

When a can containing one large ball and number of smaller ones is shaken, the rises to top, even when larger more dense than others. Similarly, mixture different sized particles will segregate by size shaken. An adaptation Monte Carlo method used study this segregation. The results show local, geometric mechanism which segregation produced. Segregation be distinguished from obvious sifting process occurs tiny grains filter down through interstices between particles.

Abstract The recently formulated weighted histogram analysis method (WHAM) 1 is an extension of Ferrenberg and Swendsen's multiple technique for free‐energy potential mean force calculations. As illustration the method, we have calculated two‐dimensional surface dihedrals gamma chi in deoxyadenosine with Monte Carlo simulations using all‐atom united‐atom representation AMBER fields. This also demonstrates one major advantages WHAM over umbrella sampling techniques. provides statistical...

Layered transition metal trichalcogenides with the chemical formula $ABX_3$ have attracted recent interest as potential candidates for two-dimensional magnets. Using first-principles calculations within density functional theory, we investigate magnetic ground states of monolayers Mn- and Cr-based semiconducting trichalcogenides. We show that second third nearest-neighbor exchange interactions ($J_2$ $J_3$) between ions, which been largely overlooked in previous theoretical studies, are...

A simplified method of applying a renormalization-group analysis to Monte Carlo simulations general systems is presented and illustrated with applications the Ising model three-state Potts model.

The Monte Carlo renormalization group is applied to the three-dimensional Ising model on simple cubic lattices with ${8}^{3}$, ${16}^{3}$, ${32}^{3}$, and ${64}^{3}$ sites. comparison of block-spin correlation functions from largest yields nearest-neighbor critical coupling ${K}_{1}^{c}=0.221654(6)$. After allowing for (i) interpolation this best estimate ${K}_{1}^{c}$, (ii) an apparent finite-size effect in renormalization-group transformation due measurement too few (seven) operators,...

The coverage of a two-dimensional surface by the random sequential adsorption hard disks is shown to approach "jamming limit" with time as ${t}^{\ensuremath{-}\frac{1}{2}}$ (or ${t}^{\ensuremath{-}\frac{1}{d}}$ for general dimension $d$), confirming conjecture Feder. same argument predicts logarithmic divergence two-particle correlation function at contact, second effects placing squares on instead disks, and consequences these results future numerical work related problems are discussed.

We obtain quasicrystalline structures in Monte Carlo simulations of a simple two-component Lennard-Jones system two dimensions. The quasicrystal, which shows tenfold symmetry, appears to be an equilibrium state the system. Although structure corresponds tiling plane with rhombuses, it is not Penrose pattern.

We suggest that the Monte Carlo renormalization group, when combined with type of cell-spin transformation introduced by van Leeuwen, should be a powerful tool in study Ising models $n>~2$. Numerical results are presented for Baxter model and nearest- next-nearest-neighbor interactions on square lattice.

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A powerful, new extension of the Monte Carlo renormalization-group (MCRG) method is used to accurately determine tricritical point and exponents in two very different two-dimensional models: an Ising antiferromagnet a Blume-Capel model. We find four relevant eigenvalues which are essentially identical for both models. also demonstrate that subtle warning signals appear standard calculation when second-order transition being misinterpreted as first order.

We present a study of the antiferromagnetic Potts model in two and three dimensions, using new method Monte Carlo simulations, which enables us to perform simulations with greatly improved efficiency. Illustrating for three-state model, we have obtained results entropy critical exponents dimensions. The low-temperature phase dimensions is shown long-range order finite-size dependence similar that XY model.

An $x\ensuremath{-}y$ model with nearest-neighbor interaction $V(\ensuremath{\theta})=2J{1\ensuremath{-}{[{cos}^{2}(\frac{\ensuremath{\theta}}{2})]}^{{p}^{2}}}$ is studied by Monte Carlo simulation. The has a transition from paramagnetic to an algebraic (massless) phase. increase of the parameter $p$, which changes shape potential, brings about change in nature continuous first order.

Monte Carlo simulations are used to study the roughening transition in solid-on-solid and discrete Gaussian models of interfaces. It is demonstrated that very long simulation times required obtain a meaningful description interface properties. Strong evidence presented for existence transition, which reflected thermodynamic properties interfaces as well expected divergence width.