Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

Rocha, J. C. S.; Schnabel, Stefan; Landau, D. P.; Bachmann, Michael

doi:10.1103/physreve.90.022601

Cited by 22 publications

(8 citation statements)

References 67 publications

(108 reference statements)

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“…As a final test to our algorithm we considered a 13 monomer flexible homopolymer, which is an intrinsically finite system with two pseudo-transitions, a first order transition at T 1st ≈ 0.33520 followed by a continuous transition at T 2nd ≈ 1.1292 [32]. In this model, we considered that unbounded monomers interacts via a truncated and shifted Lennard-Jones potential,…”

Section: Monomer Homopolymer Modelmentioning

confidence: 99%

“…We follow Ref. [32] to set the parameters to R = 0.3, r 0 = 0.7, and K = 40. The histograms were obtained from the density of states by using the conventional Wang-Landau algorithm [14].…”

Section: Monomer Homopolymer Modelmentioning

confidence: 99%

“…A low temperature first order and a second at higher temperature. The transition temperatures are to be compared with those in Ref [32]…”

mentioning

confidence: 99%

See 2 more Smart Citations

Energy probability distribution zeros: A route to study phase transitions

Costa¹,

Mól²,

Rocha³

2017

Computer Physics Communications

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In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties. homopolymer system. Our choice cover systems with first order, continuous and Berezinskii-Kosterlitz-Thouless transitions as well as the homopolymer that has two pseudo-transitions. The strategy can easily be adapted to any model, classical or quantum, once we are able to build the corresponding energy probability distribution.

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Section: Monomer Homopolymer Modelmentioning

confidence: 99%

“…We follow Ref. [32] to set the parameters to R = 0.3, r 0 = 0.7, and K = 40. The histograms were obtained from the density of states by using the conventional Wang-Landau algorithm [14].…”

Section: Monomer Homopolymer Modelmentioning

confidence: 99%

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Energy probability distribution zeros: A route to study phase transitions

Costa¹,

Mól²,

Rocha³

2017

Computer Physics Communications

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“…A microcanonical analysis reveals and allows us to classify pseudo-phase transitions [21]. Results of such an analysis, carried out for different polymeric systems, can be found, for instance, in the works [10,11,25,27,28,31,32,45,47,48,49,50]. However, one should note that traditionally, Monte Carlo methods work in the configuration (conformation) space, so that the accumulated DoS is the “conformational” one, and the notion “conformational” microcanonical (NVU) ensemble can be used [51].…”

Section: Model and Simulation Techniquesmentioning

confidence: 99%

Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

et al. 2019

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The combination of flexibility and semiflexibility in a single molecule is a powerful design principle both in nature and in materials science. We present results on the conformational behavior of a single multiblock-copolymer chain, consisting of equal amounts of Flexible (F) and Semiflexible (S) blocks with different affinity to an implicit solvent. We consider a manifold of macrostates defined by two terms in the total energy: intermonomer interaction energy and stiffness energy. To obtain diagrams of states (pseudo-phase diagrams), we performed flat-histogram Monte Carlo simulations using the Stochastic Approximation Monte Carlo algorithm (SAMC). We have accumulated two-Dimensional Density of States (2D DoS) functions (defined on the 2D manifold of macrostates) for a SF-multiblock-copolymer chain of length N = 64 with block lengths b = 4, 8, 16, and 32 in two different selective solvents. In an analysis of the canonical ensemble, we calculated the heat capacity and determined its maxima and the most probable morphologies in different regions of the state diagrams. These are rich in various, non-trivial morphologies, which are formed without any specific interactions, and depend on the block length and the type of solvent selectivity (preferring S or F blocks, respectively). We compared the diagrams with those for the non-selective solvent and reveal essential changes in some cases. Additionally, we implemented microcanonical analysis in the “conformational” microcanonical ( N V U , where U is the potential energy) and the true microcanonical ( N V E , where E is the total energy) ensembles with the aim to reveal and classify pseudo-phase transitions, occurring under the change of temperature.

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“…Fundamental aspects of phase transitions in complex systems can be revealed by the analysis of its microcanonical thermostatistics [1,2], which is characterised by the well known entropy S(E) = k B ln Ω(E), where Ω(E) denotes the density of states of a system with energy E. In particular, the analysis of inflection points of the microcanonical inverse temperature β(E) = dS(E)/dE plays an important role in the identification of stable, unstable and metastable regions in the phase diagram [3][4][5], providing alternative insights to the usual canonical analysis. Also, free-energy profiles can be obtained from the caloric curves β vs E, from where one can easily evaluate the values of barrier heights and latent heats.…”

Section: Introductionmentioning

confidence: 99%

Microcanonical thermostatistics analysis without histograms: Cumulative distribution and Bayesian approaches

Alves

Morero

Rizzi

2015

Computer Physics Communications

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Microcanonical thermostatistics analysis has become an important tool to reveal essential aspects of phase transitions in complex systems. An efficient way to estimate the microcanonical inverse temperature β(E) and the microcanonical entropy S (E) is achieved with the statistical temperature weighted histogram analysis method (ST-WHAM). The strength of this method lies on its flexibility, as it can be used to analyse data produced by algorithms with generalised sampling weights. However, for any sampling weight, ST-WHAM requires the calculation of derivatives of energy histograms H(E), which leads to non-trivial and tedious binning tasks for models with continuous energy spectrum such as those for biomolecular and colloidal systems. Here, we discuss two alternative methods that avoid the need for such energy binning to obtain continuous estimates for H(E) in order to evaluate β(E) by using ST-WHAM: (i) a series expansion to estimate probability densities from the empirical cumulative distribution function (CDF), and (ii) a Bayesian approach to model this CDF. Comparison with a simple linear regression method is also carried out. The performance of these approaches is evaluated considering coarse-grained protein models for folding and peptide aggregation.

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Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

Cited by 22 publications

References 67 publications

Energy probability distribution zeros: A route to study phase transitions

Energy probability distribution zeros: A route to study phase transitions

Diagrams of States of Single Flexible-Semiflexible Multi-Block Copolymer Chains: A Flat-Histogram Monte Carlo Study

Microcanonical thermostatistics analysis without histograms: Cumulative distribution and Bayesian approaches

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