Free energies of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:mrow></mml:math>model from Wang-Landau simulations

Tröster, A.; Dellago, Christoph; Schranz, W.

doi:10.1103/physrevb.72.094103

Cited by 42 publications

(46 citation statements)

References 28 publications

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“…1, which gives an artist's impression of a Landau free energy as a function of a onedimensional order parameter as the system crosses the critical temperature Tc. For T > Tc the order parameter fluctuations are predominantly Gaussian and the effect of the non-Gaussian quartic term is hidden in the tail of the distribution, as pointed out also by other authors (10,13). By using a p(s) that is broader than the natural Gaussian fluctuations, we can enhance the probability with which the tails are sampled, thus improving the computation of the parameter b proportional to the quartic term I4(s).…”

Section: Bias Potential and Target Distributionmentioning

confidence: 73%

“…An advantage of using this model is that its strengths and limits are well known and that other researchers have already attempted to perform such a calculation (8)(9)(10)(11)(12)(13)(14). A system that undergoes a second-order phase transition is described in the GL model by the following free energy, valid in a rotationally invariant one-component real-order parameter scenario,…”

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confidence: 99%

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Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Invernizzi

Valsson

Parrinello

2017

Proc. Natl. Acad. Sci. U.S.A.

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A powerful way to deal with a complex system is to build a coarsegrained model capable of catching its main physical features, while being computationally affordable. Inevitably, such coarsegrained models introduce a set of phenomenological parameters, which are often not easily deducible from the underlying atomistic system. We present a unique approach to the calculation of these parameters, based on the recently introduced variationally enhanced sampling method. It allows us to obtain the parameters from atomistic simulations, providing thus a direct connection between the microscopic and the mesoscopic scale. The coarsegrained model we consider is that of Ginzburg-Landau, valid around a second-order critical point. In particular, we use it to describe a Lennard-Jones fluid in the region close to the liquidvapor critical point. The procedure is general and can be adapted to other coarse-grained models.coarse graining | enhanced sampling | Ginzburg-Landau free energy | second-order phase transitions | Lennard-Jones C omputer simulations of condensed systems based on an atomistic description of matter are playing an everincreasing role in many fields of science. However, as the complexity of the systems studied increases, so does the awareness that a less detailed, but nevertheless accurate, description of the system is necessary.This has been long since recognized, and branches of physics like elasticity or hydrodynamics can be classified in modern terms as coarse-grained (CG) models of matter. In more recent times, a field theoretical model suitable to describe second-order phase transitions has been introduced by Landau (1) and later perfected by Ginzburg (2). In recent decades a number of coarsegrained models that aim at describing polymers or biomolecules have also been proposed (3,4). In all these approaches some degrees of freedom, deemed not essential to study the phenomenon at hand, are integrated out and the resulting reduced description contains a number of parameters that are not easily determined.Here we use the recently developed variationally enhanced sampling (VES) method (5) to suggest a procedure that allows the determination of such parameters, starting from the microscopic Hamiltonian. This illuminates a somewhat unexpected application of VES, which has been introduced as an enhanced sampling method. We show that it also provides a powerful framework for the optimization of CG models, due to the combination of its enhanced sampling capabilities and its variational flexibility. Moreover, VES takes advantage of its deep connection with relative entropy, a quantity that has been shown to play a key role in multiscale problems (6, 7).As a first test case for our procedure we consider the Ginzburg-Landau (GL) model for continuous phase transitions. An advantage of using this model is that its strengths and limits are well known and that other researchers have already attempted to perform such a calculation (8)(9)(10)(11)(12)(13)(14). A system that undergoes a second-order phase transition is desc...

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Section: Bias Potential and Target Distributionmentioning

confidence: 73%

mentioning

confidence: 99%

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Invernizzi

Valsson

Parrinello

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…2. When the relative position of the interfaces change within the two-phase regime, G i and N i can be replaced by an constant if "wiggles" can be neglected (wiggles [19,20] are discussed later in the paper). Thus combining the last two equations gives…”

Section: Figmentioning

confidence: 99%

“…There are, however, two effects that may spoil this assumption: i) if the distance between the interfaces is sufficiently small, particles in one (or both) phases will not have bulk properties, and ii) "wiggles" on G(N s ) [19,20]. To exemplify the latter effect think of a square lattice gas with attractions between neighboring particles.…”

Section: E Gibbs Free Energy Dependency Of the Interface Positions Rmentioning

confidence: 99%

Determining the phase diagram of water from direct coexistence simulations: The phase diagram of the TIP4P/2005 model revisited

Conde

Gonzalez

Abascal

et al. 2013

The Journal of Chemical Physics

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Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs. I. INTRODUCTIONAn important aspect of computational condensed matter physics is to compute phase diagrams of model systems. The naive approach is to preform a long-time simulation at a selected state point and hope that the system by itself finds its preferred phase, i.e. the phase with the lowest Gibbs free energy. In most cases this strategy is not viable since first-order transitions are associated with hysteresis. Thus the system is likely to be stuck in a metastable phase. The origin of this hysteresis effect is the formation of an interface between two phases. The surface tension of the interface gives rise to a free energy barrier that the system has to overcome to transform from one phase to the other [1]. A conceptual appealing and widely used strategy to overcome the hysteresis problem is to preform simulations starting from an initial configuration with two phases in a periodic box [2][3][4][5][6][7][8][9][10][11][12][13][14]. When a steady state situation is reached the stable phase will grow at the expense of the other phase. The disadvantages of this approach are that: i) it relates to a non-equilibrium computation that cannot be done ad infinitum; ii) a sufficiently large system is needed to reach the steady state growth; iii) thermal fluctuation will result in some probability that the system will move towards the disfavored phase. In a recent paper [15] these problems were resolved by introducing the so-called "interface pinning" (IP) method. In short, the idea of this method is to compute the average force needed to keep the system in the two-phases state. This is done by connecting the system to a harmonic field which couples to an order-parameter that distinguished between the two phases of interest. The Gibbs free energy difference between the phases is determined by the average force that the applied field exerts on the system. Thus, a standard * ulf.pedersen@tuwien.ac.at ad infinitum equilibrium simulation gives the information needed to computed the Gibbs free energy difference between the two phases of interest.The purpose of this paper is to give a detailed ...

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“…Specifically, we wish to highlight recent work by Tro¨ster et al (2005) on the f 4 model; by means of Wang-Landau simulations, these authors discover plateaus in the energetic landscape far from equilibrium and motivate these findings. They point out the inadequacy of a polynomial interpolation in this context.…”

Section: Introductionmentioning

confidence: 95%

On Landau theory and symmetric energy landscapes for phase transitions

Hormann

Zimmer

2007

Journal of the Mechanics and Physics of Solids

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The aim of this presentation is the development of a general approach for modelling the global complex energy landscapes of phase transitions. For the sake of clarity and brevity the exposition is restricted to martensitic phase transition (i.e., diffusionless phase transitions in crystalline solids). The methods, however, are more broadly applicable. Explicit energy functions are derived for the cubic-to-tetragonal phase transition, where data are fitted for InTl. Another example is given for the cubic-to-monoclinic transition in CuZnAl. The resulting energies are defined globally, in a piecewise manner. We use splines that are twice continuously differentiable to ensure sufficient smoothness. The modular (piecewise) technique advocated here allows for modelling elastic moduli, energy barriers and other characteristics independent of each other. r

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Free energies of theϕ4model from Wang-Landau simulations

Cited by 42 publications

References 28 publications

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Coarse graining from variationally enhanced sampling applied to the Ginzburg–Landau model

Determining the phase diagram of water from direct coexistence simulations: The phase diagram of the TIP4P/2005 model revisited

On Landau theory and symmetric energy landscapes for phase transitions

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