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Lee JH, Kim SY, Lee J. Partition function zeros of a square-lattice homopolymer with nearest- and next-nearest-neighbor interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052601. [PMID: 23767558 DOI: 10.1103/physreve.87.052601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2013] [Indexed: 06/02/2023]
Abstract
We study distributions of the partition function zeros in the complex temperature plane for a square-lattice homopolymer with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. The dependence of distributions on the ratio of NN and NNN interaction strengths R is examined. The finite-size scaling of the zeros is performed to obtain the crossover exponent, which is shown to be independent of R within error bars, suggesting that all of these models belong to the same universality class. The transition temperatures are also computed by the zeros to obtain the phase diagram, and the results confirm that the model with stronger NNN interaction exhibits stronger effects of cooperativity.
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Affiliation(s)
- Jae Hwan Lee
- School of Systems Biomedical Science and Department of Bioinformatics and Life Science, Soongsil University, Seoul 156-743, Korea
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Lee JH, Kim SY, Lee J. Collapse transition of a square-lattice polymer with next nearest-neighbor interaction. J Chem Phys 2011; 135:204102. [DOI: 10.1063/1.3663712] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Lee JH, Kim SY, Lee J. Exact partition function zeros and the collapse transition of a two-dimensional lattice polymer. J Chem Phys 2010; 133:114106. [PMID: 20866125 DOI: 10.1063/1.3486176] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jae Hwan Lee
- Department of Bioinformatics and Life Science and School of Systems Biomedical Science, Soongsil University, Seoul 156-743, Korea
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Cunha-Netto AG, Caparica AA, Tsai SH, Dickman R, Landau DP. Improving Wang-Landau sampling with adaptive windows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:055701. [PMID: 19113183 DOI: 10.1103/physreve.78.055701] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2008] [Indexed: 05/27/2023]
Abstract
Wang-Landau sampling (WLS) of large systems requires dividing the energy range into "windows" and joining the results of simulations in each window. The resulting density of states (and associated thermodynamic functions) is shown to suffer from boundary effects in simulations of lattice polymers and the five-state Potts model. Here, we implement WLS using adaptive windows. Instead of defining fixed energy windows (or windows in the energy-magnetization plane for the Potts model), the boundary positions depend on the set of energy values on which the histogram is flat at a given stage of the simulation. Shifting the windows each time the modification factor f is reduced, we eliminate border effects that arise in simulations using fixed windows. Adaptive windows extend significantly the range of system sizes that may be studied reliably using WLS.
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Affiliation(s)
- A G Cunha-Netto
- Instituto de Física, Universidade Federal de Goiás, C.P. 131, 74001-970 Goiânia, Brazil.
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Narasimhan SL, Krishna PSR, Ponmurugan M, Murthy KPN. A growth walk model for estimating the canonical partition function of interacting self-avoiding walk. J Chem Phys 2008; 128:014105. [DOI: 10.1063/1.2806935] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Narasimhan SL, Krishna PSR, Rajarajan AK, Murthy KPN. Interacting growth walk: a model for hyperquenched homopolymer glass? PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:011802. [PMID: 12636522 DOI: 10.1103/physreve.67.011802] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2002] [Indexed: 05/24/2023]
Abstract
We show that the compact self-avoiding walk configurations, kinetically generated by the recently introduced interacting growth walk (IGW) model, can be considered as members of a canonical ensemble if they are assigned random values of energy. Such a mapping is necessary for studying the thermodynamic behavior of this system. We have presented the specific heat data for the IGW, obtained from extensive simulations on a square lattice; we observe a broad hump in the specific heat above the theta point, contrary to expectation.
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Affiliation(s)
- S L Narasimhan
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai-400 085, India.
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Ishinabe T. Examination of the theta -point from exact enumeration of self-avoiding walks. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/18/16/019] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Kholodenko AL, Freed KF. Conformational space renormalisation group theory of 'tricritical' (theta point) exponents for a polymer chain. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/17/4/007] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Cattarinussi S, Jug G. Coil-globule transition temperature enhancement in a polymer molecule adsorbed to a wall. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/23/12/043] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Kholodenko AL, Freed KF. Coil-globule transition: comparison of field theoretic and conformational space formulations. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/17/13/022] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Privman V. Study of the θ point by enumeration of self-avoiding walks on the triangular lattice. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/19/16/027] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Derrida B, Saleur H. Collapse of two-dimensional linear polymers: a transfer matrix calculation of the exponent νt. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/18/17/003] [Citation(s) in RCA: 66] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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17
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Ishinabe T. Examination of the theta -point from exact enumeration of self-avoiding walks. II. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/20/18/041] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Dhar D, Vannimenus J. The collapse transition of linear polymers on fractal lattices. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/20/1/028] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Termonia Y. Molecular Modeling of Structure Development upon Quenching of a Polymer Solution. Macromolecules 1997. [DOI: 10.1021/ma970565o] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yves Termonia
- Central Research and Development, Experimental Station, E. I. du Pont de Nemours, Inc., Wilmington, Delaware 19880-0356
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Wittkop M, Kreitmeier S, Göritz D. The collapse transition of a single polymer chain in two and three dimensions: A Monte Carlo study. J Chem Phys 1996. [DOI: 10.1063/1.471041] [Citation(s) in RCA: 69] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Torres AM, Rubio AM, Freire JJ, Bishop M, Clarke JHR. Theta state and collapse of off‐lattice chains in two dimensions. J Chem Phys 1994. [DOI: 10.1063/1.466818] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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O’Toole EM, Panagiotopoulos AZ. Effect of sequence and intermolecular interactions on the number and nature of low‐energy states for simple model proteins. J Chem Phys 1993. [DOI: 10.1063/1.464091] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Dickman R. Equation of state of two‐dimensional lattice chains at the theta point. J Chem Phys 1992. [DOI: 10.1063/1.462135] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Brender C. Coil to rod transitions in Monte Carlo simulations of a short polyelectrolyte. III. Contact as a new type of bond. J Chem Phys 1991. [DOI: 10.1063/1.459790] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Universality of properties of coil-globule transitions in different two-dimensional lattice models of a macromolecule. POLYMER 1991. [DOI: 10.1016/0032-3861(91)90544-s] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Kumar S, Singh Y. Collapse transition of linear polymers on a family of truncated n-simplex lattices. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:7151-7154. [PMID: 9904028 DOI: 10.1103/physreva.42.7151] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Wu K, Bradley RM. Collapse transition of self-avoiding walks and trails by real-space renormalization. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:6845-6851. [PMID: 9903098 DOI: 10.1103/physreva.41.6845] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Maes D, Vanderzande C. Self-avoiding rings at the theta point. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:3074-3080. [PMID: 9903460 DOI: 10.1103/physreva.41.3074] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Chang IS, Meirovitch H, Shapir Y. Tricritical trails on a square lattice with impenetrable linear boundary: Computer simulation and analytic bounds. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:1808-1822. [PMID: 9903290 DOI: 10.1103/physreva.41.1808] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Bradley RM. Exact theta point and exponents for two models of polymer chains in two dimensions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:914-922. [PMID: 9903172 DOI: 10.1103/physreva.41.914] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Meirovitch H, Lim HA. The collapse transition of self‐avoiding walks on a square lattice: A computer simulation study. J Chem Phys 1989. [DOI: 10.1063/1.457014] [Citation(s) in RCA: 66] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Meirovitch H, Lim HA. Computer simulation of trails on a square lattice. II. Finite temperatures and the collapse transition. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:4186-4194. [PMID: 9901748 DOI: 10.1103/physreva.39.4186] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Milik M, Orszagh A. Monte Carlo model of a polymer chain attached to an interface in poor solvent conditions. POLYMER 1989. [DOI: 10.1016/0032-3861(89)90155-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Poole PH, Coniglio A, Jan N, Stanley HE. Universality classes of the theta and theta ' points. PHYSICAL REVIEW. B, CONDENSED MATTER 1989; 39:495-504. [PMID: 9947179 DOI: 10.1103/physrevb.39.495] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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de Queiroz SLA. Coarse-grained Flory approximation for a polymer chain at the FTHETA point in two dimensions. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:430-433. [PMID: 9901040 DOI: 10.1103/physreva.39.430] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Meirovitch H, Lim HA. Tricritical exponents for trails on a square lattice obtained by the scanning simulation method. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:1670-1672. [PMID: 9900564 DOI: 10.1103/physreva.38.1670] [Citation(s) in RCA: 27] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Vanderzande C. Superconformal invariance in the tricritical O(N) model. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:2865-2867. [PMID: 9946609 DOI: 10.1103/physrevb.38.2865] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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39
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Bishop M. The collapse transition for two‐dimensional linear and ring polymers. J Chem Phys 1988. [DOI: 10.1063/1.455695] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Seno F, Stella A. θ point of a linear polymer in 2 dimensions: a renormalization group analysis of Monte Carlo enumerations. ACTA ACUST UNITED AC 1988. [DOI: 10.1051/jphys:01988004905073900] [Citation(s) in RCA: 92] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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Duplantier B, Saleur H. Exact tricritical exponents for polymers at the FTHETA point in two dimensions. PHYSICAL REVIEW LETTERS 1987; 59:539-542. [PMID: 10035800 DOI: 10.1103/physrevlett.59.539] [Citation(s) in RCA: 115] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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43
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Coniglio A, Jan N, Majid I, Stanley HE. Conformation of a polymer chain at the theta' point: Connection to the external perimeter of a percolation cluster. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:3617-3620. [PMID: 9941867 DOI: 10.1103/physrevb.35.3617] [Citation(s) in RCA: 115] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Birshtein T, Buldyrev S, Elyashevitch A. Monte-Carlo simulation of the collapse transition of a two-dimensional polymer. POLYMER 1985. [DOI: 10.1016/0032-3861(85)90008-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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49
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Kremer K, Lyklema JW. Indefinitely growing self-avoiding walk. PHYSICAL REVIEW LETTERS 1985; 54:267-269. [PMID: 10031464 DOI: 10.1103/physrevlett.54.267] [Citation(s) in RCA: 33] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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50
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Kholodenko AL, Freed KF. Theta point (‘‘tricritical’’) region behavior for a polymer chain: Transition to collapse. J Chem Phys 1984. [DOI: 10.1063/1.446748] [Citation(s) in RCA: 78] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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