A scaling theory of the collapse transition in geometric cluster models of polymers and vesicles

Brak, R; Owczarek, A L; Prellberg, Thomas

doi:10.1088/0305-4470/26/18/022

Cited by 58 publications

(28 citation statements)

References 31 publications

(70 reference statements)

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“…The non-analytic part of the extensive free energy of self-interacting polymers in the proximity of the transition is, by scaling arguments 30 , of the form…”

Section: Resultsmentioning

confidence: 99%

First-order coil-globule transition driven by vibrational entropy

et al. 2012

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By shifting the balance between conformational entropy and internal energy, polymers modify their shape under external stimuli, such as changes in temperature. Prominent among such transformations is the coil-globule transition, whereby a polymer can switch from an entropydominated coil conformation to a globular one, governed by energy. The nature of the coilglobule transition has remained elusive, with evidence for both continuous and discontinuous transitions, with the two-state behaviour of proteins as an instance of the latter. Theoretical models mostly predict second-order transitions. Here we introduce a model that takes into consideration hitherto neglected features common to any polymer. We show that a firstorder phase transition smoothly appears as a function of the model parameters. our results can relieve part of the conflicts between theory and experiments in the field of protein folding, in the wake of recent studies tracing back the remarkable properties of proteins to basic polymer physics.

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“…The non-analytic part of the extensive free energy of self-interacting polymers in the proximity of the transition is, by scaling arguments 30 , of the form…”

Section: Resultsmentioning

confidence: 99%

First-order coil-globule transition driven by vibrational entropy

et al. 2012

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“…i) The slope of the critical curve x c (q) is determined by s c and by φ. The phenomenon that the slope of the critical coincides with the exponent φ is also called hyperscaling relation [15,42].…”

Section: We Then Havementioning

confidence: 99%

Limit Distributions and Scaling Functions

Richard

2009

Polygons, Polyominoes and Polycubes

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We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs with the same probability. We relate limit distributions to the scaling behaviour of the associated perimeter and area generating functions, thereby providing a geometric interpretation of scaling functions. To a major extent, this article is a pedagogic review of known results.

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“…This corresponds to a weak singularity for the specific heat measured along the critical line, as the associated exponent α [53] is negative:…”

Section: Critical Line and Crossover Exponentmentioning

confidence: 99%

On directed interacting animals and directed percolation

Knežević

Vannimenus

2002

J. Phys. A: Math. Gen.

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Abstract.We study the phase diagram of fully directed lattice animals with nearest-neighbour interactions on the square lattice. This model comprises several interesting ensembles (directed site and bond trees, bond animals, strongly embeddable animals) as special cases and its collapse transition is equivalent to a directed bond percolation threshold. Precise estimates for the animal size exponents in the different phases and for the critical fugacities of these special ensembles are obtained from a phenomenological renormalization group analysis of the correlation lengths for strips of width up to n = 17. The crossover region in the vicinity of the collapse transition is analyzed in detail and the crossover exponent φ is determined directly from the singular part of the free energy. We show using scaling arguments and an exact relation due to Dhar that φ is equal to the Fisher exponent σ governing the size distribution of large directed percolation clusters.

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A scaling theory of the collapse transition in geometric cluster models of polymers and vesicles

Cited by 58 publications

References 31 publications

First-order coil-globule transition driven by vibrational entropy

First-order coil-globule transition driven by vibrational entropy

Limit Distributions and Scaling Functions

On directed interacting animals and directed percolation

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