Monte carlo study of the interacting self-avoiding walk model in three dimensions

Tesi, Maria Carla; Rensburg, E J Janse van; Orlandini, Enzo; Whittington, S G

doi:10.1007/bf02189229

Cited by 299 publications

(234 citation statements)

References 30 publications

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“…Another successful family of techniques aims at obtaining D(E) by changing iteratively the probability with which the various energy levels are visited in stochastic dynamics until the recorded energy histogram is "flat". Such methods include entropic sampling [4], multicanonical and broad-histogram techniques techniques [3,5] and also the recent method of Wang and Landau [6].These and similar techniques have proved to be very valuable in a variety of contexts [7,8,9], but there is still ample scope for alternative approaches that could provide improved efficiency and better error control. Here we propose to modify and extend the metadynamics method recently introduced by two of us [10] for evaluating D(E).…”

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confidence: 99%

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Reconstructing the Density of States by History-Dependent Metadynamics

2004

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We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free energy profile of a canonical system to be recovered within a pre-assigned accuracy, [A. Laio and M. Parrinello, PNAS 2002]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50x50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.It has long been recognized that all energy-related thermodynamic properties of a classical canonical system can be calculated once the energy density of states D(E) is known. In fact, starting from the partition function Z = dE D(E)e −βE , quantities like free energies, specific heats and phase transition temperatures can be computed in a straightforward manner. In principle, all canonical averages can be calculated through a multidimensional density of states. Due to this central role in equilibrium thermodynamics a variety of theoretical and computations studies have addressed the problem of how to obtain D(E) (or, equivalently, the entropy profile S(E) = ln(D(E)) in a reliable and efficient way.In principle, D(E) could be calculated from the histogram of the energies visited during a single "very long" constanttemperature simulation [1]. In practice, for any finite simulation only a limited energy windows is sampled so that the recovery of the system thermodynamics over a wide temperature range is unfeasible.Several alternative strategies have been developed to remedy this shortcoming. For example the multiple histogram reweighting technique relies on performing several simulations at different temperatures, so as to explore different (overlapping) energy intervals [2]. The various histograms are then optimally combined to obtain D(E) over the union of the energy intervals. Another successful family of techniques aims at obtaining D(E) by changing iteratively the probability with which the various energy levels are visited in stochastic dynamics until the recorded energy histogram is "flat". Such methods include entropic sampling [4], multicanonical and broad-histogram techniques techniques [3,5] and also the recent method of Wang and Landau [6].These and similar techniques have proved to be very valuable in a variety of contexts [7,8,9], but there is still ample scope for alternative approaches that could provide improved efficiency and better error control. Here we propose to modify and extend the metadynamics method recently introduced by two of us [10] for evaluating D(E). The algorithm we introduce allows a good error control on the explored energy range. Moreover, although within our approach D(E) could be reconstructed ...

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confidence: 99%

“…These and similar techniques have proved to be very valuable in a variety of contexts [7,8,9], but there is still ample scope for alternative approaches that could provide improved efficiency and better error control. Here we propose to modify and extend the metadynamics method recently introduced by two of us [10] for evaluating D(E).…”

mentioning

confidence: 99%

Reconstructing the Density of States by History-Dependent Metadynamics

2004

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“…of 0.1. Finally, as in our study of the peptide system, we employ a measure similar to the chisquare measure, the integrated squared error of the spatial density, (4) to demonstrate the sampling efficiency of the REM and SREM. Here, K = 1000 is the number of bins used to calculate χ S 2(t) with respect to the spatial coordinate, which is independent of the number of bins in the PEDF histogram, N. The normalized densities are calculated only for the replica at kT, and there is no averaging over the three ensembles.…”

Section: Discussionmentioning

confidence: 99%

Serial Replica Exchange

et al. 2007

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Parallel tempering (or the replica exchange method (REM)) is a powerful method for speeding up the sampling of conformational states of systems with rough energy landscapes, like proteins, where stable conformational states can be separated by large energy barriers. The usual implementation of the REM is performed on local computer clusters (or parallel processors) where the different replicas must be run synchronously. Here, we present serial replica exchange (SREM), a method that is equivalent to the standard REM in terms of efficiency yet runs asynchronously on a distributed network of computers. A second advantage is the method's greatly enhanced fault tolerance, which enables the study of biological systems on worldwide distributed computing environments, such as Folding@Home. 1 For proof of concept, we apply the SREM to a single alanine dipeptide molecule in explicit water. We show that the SREM reproduces the thermodynamic and structural properties determined by the REM.

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“…where ν t and φ t are the tricritical metric and crossover exponents, respectively, τ i ≡ |β i − β i,Θ |, and f (x) is a scaling function, expected to behave as [50][51][52] …”

Section: Models and Quantities Of Interestmentioning

confidence: 99%

Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge

Rodrigues

2017

Phys. Rev. E

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We present results from extensive Monte Carlo simulations of polymer models where each lattice site can be visited by up to K monomers and no restriction is imposed on the number of bonds on each lattice edge. These multiple monomer per site (MMS) models are investigated on the square and cubic lattices, for K = 2 and K = 3, by associating Boltzmann weights ω0 = 1, ω1 = e β 1 and ω2 = e β 2 to sites visited by 1, 2 and 3 monomers, respectively. Two versions of the MMS models are considered for which immediate reversals of the walks are allowed (RA) or forbidden (RF). In contrast to previous simulations of these models, we find the same thermodynamic behavior for both RA and RF versions. In three-dimensions, the phase diagrams -in space β2 × β1 -are featured by coil and globule phases separated by a line of Θ points, as thoroughly demonstrated by the metric νt, crossover φt and entropic γt exponents. The existence of the Θ-lines is also confirmed by the second virial coefficient. This shows that no discontinuous collapse transition exists in these models, in contrast to previous claims based on a weak bimodality observed in some distributions, which indeed exists in a narrow region very close to the Θ-line when β1 < 0. Interestingly, in two-dimensions, only a crossover is found between the coil and globule phases.

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Monte carlo study of the interacting self-avoiding walk model in three dimensions

Cited by 299 publications

References 30 publications

Reconstructing the Density of States by History-Dependent Metadynamics

Reconstructing the Density of States by History-Dependent Metadynamics

Serial Replica Exchange

Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge

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