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Oliveira TJ, Stilck JF. Nature of the collapse transition in interacting self-avoiding trails. Phys Rev E 2016; 93:012502. [PMID: 26871113 DOI: 10.1103/physreve.93.012502] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2015] [Indexed: 11/07/2022]
Abstract
We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination q and on a Husimi lattice built with squares and coordination q=4. The exact grand-canonical solutions of the model are obtained, considering that up to K monomers can be placed on a site and associating a weight ω_{i} with an i-fold visited site. Very rich phase diagrams are found with nonpolymerized, regular polymerized, and dense polymerized phases separated by lines (or surfaces) of continuous and discontinuous transitions. For a Bethe lattice with q=4 and K=2, the collapse transition is identified with a bicritical point and the collapsed phase is associated with the dense polymerized (solidlike) phase instead of the regular polymerized (liquidlike) phase. A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISATs and for interacting self-avoiding walks on the square lattice. For q=6 and K=3 (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.
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Affiliation(s)
- Tiago J Oliveira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
| | - Jürgen F Stilck
- Instituto de Física and National Institute of Science and Technology for Complex Systems, Universidade Federal Fluminense, Avenida Litorânea s/n, 24210-346 Niterói, Rio de Janeiro, Brazil
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Oliveira TJ, Stilck JF. Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032101. [PMID: 26465420 DOI: 10.1103/physreve.92.032101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2015] [Indexed: 06/05/2023]
Abstract
Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.
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Affiliation(s)
- Tiago J Oliveira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900, Viçosa, MG, Brazil
| | - Jürgen F Stilck
- Instituto de Física and National Institute of Science and Technology for Complex Systems, Universidade Federal Fluminense, Av. Litorânea s/n, 24210-346, Niterói, RJ, Brazil
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Knežević M, Knežević D. Large scale behavior of a two-dimensional model of anisotropic branched polymers. J Chem Phys 2013; 139:164904. [PMID: 24182076 DOI: 10.1063/1.4826348] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study critical properties of anisotropic branched polymers modeled by semi-directed lattice animals on a triangular lattice. Using the exact transfer-matrix approach on strips of quite large widths and phenomenological renormalization group analysis, we obtained pretty good estimates of various critical exponents in the whole high-temperature region, including the point of collapse transition. Our numerical results suggest that this collapse transition belongs to the universality class of directed percolation.
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Affiliation(s)
- Milan Knežević
- Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade, Serbia
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Janssen HK, Stenull O. Collapse transition of randomly branched polymers: renormalized field theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051126. [PMID: 21728509 DOI: 10.1103/physreve.83.051126] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2011] [Indexed: 05/31/2023]
Abstract
We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well-established dimensional-reduction results from a different angle. For the collapse θ transition, we uncover a hidden Becchi-Rouet-Stora supersymmetry, signaling the sole relevance of tree configurations. We correct the long-standing one-loop results for the critical exponents, and we push these results on to two-loop order. For the collapse θ' transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions.
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Affiliation(s)
- Hans-Karl Janssen
- Institut für Theoretische Physik III, Heinrich-Heine-Universität, Düsseldorf, Germany
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Janssen HK, Wevelsiep F, Stenull O. Renormalized field theory of collapsing directed randomly branched polymers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:041809. [PMID: 19905335 DOI: 10.1103/physreve.80.041809] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2009] [Indexed: 05/28/2023]
Abstract
We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with epsilon expansion that this transition belongs to the same universality class as directed percolation.
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Affiliation(s)
- Hans-Karl Janssen
- Institut für Theoretische Physik III, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany
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Foster DP, Pinettes C. A corner transfer matrix renormalization group investigation of the vertex-interacting self-avoiding walk model. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/41/003] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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8
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Foster DP, Seno F. Two-dimensional self-avoiding walk with hydrogen-like bonding: phase diagram and critical behaviour. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/47/302] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Machado KD, de Oliveira MJ, Stilck JF. Thermodynamic behavior of a polymer with interacting bonds on a square lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:051810. [PMID: 11735961 DOI: 10.1103/physreve.64.051810] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2000] [Revised: 07/03/2001] [Indexed: 05/23/2023]
Abstract
Using the transfer matrix technique, finite-size scaling, phenomenological renormalization group, and conformal invariance ideas, the thermodynamic behavior of a polymer with interacting bonds on a square lattice has been studied. In this model, one monomer that belongs to the polymer has an activity x=e(beta(mu)), while the interactions between bonds of the polymer that are located on opposite edges of elementary squares of the lattice have a statistical weight y=e(-beta(epsilon)), where epsilon is the interaction energy. Next, the phase diagram of the model in the (x,y) plane was found, which shows three phases, two of them being polymerized. Furthermore, the densities of occupied sites and of bond interactions in each phase were calculated, in order to determine the nature of the transitions between the phases. The results obtained are consistent with a second-order transition line between the nonpolymerized and the regular polymerized phase and a first-order transition between the nonpolymerized and the dense polymerized phase. The boundary between both polymerized phases may be of first or second order, and thus evidence for a tricritical point is found.
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Affiliation(s)
- K D Machado
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318 05315-970-São Paulo, São Paulo, Brazil
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Tabak F, Corti M, Pavesi L, Rigamonti A. Nuclear magnetic resonance relaxation of polyacrylamide gels around the collapse transition. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0022-3719/20/34/008] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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11
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Causo MS, Coluzzi B, Grassberger P. Simple model for the DNA denaturation transition. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:3958-3973. [PMID: 11088917 DOI: 10.1103/physreve.62.3958] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/1999] [Indexed: 05/23/2023]
Abstract
We study pairs of interacting self-avoiding walks ¿omega(1), omega(2)¿ on the 3d simple cubic lattice. They have a common origin omega(1)(0)=omega 20, and are allowed to overlap only at the same monomer position along the chain: omega(1)(i) not equal omega(2)(j) for i not equal j, while omega(1)(i)=omega(2)(i) is allowed. The latter overlaps are indeed favored by an energetic gain epsilon. This is inspired by a model introduced long ago by Poland and Sheraga [J. Chem. Phys. 45, 1464 (1966)] for the denaturation transition in DNA where, however, self avoidance was not fully taken into account. For both models, there exists a temperature T(m) above which the entropic advantage to open up overcomes the energy gained by forming tightly bound two-stranded structures. Numerical simulations of our model indicate that the transition is of first order (the energy density is discontinuous), but the analog of the surface tension vanishes and the scaling laws near the transition point are exactly those of a second-order transition with crossover exponent straight phi=1. Numerical and exact analytic results show that the transition is second order in modified models where the self-avoidance is partially or completely neglected.
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Affiliation(s)
- M S Causo
- John von Neumann-Institut für Computing (NIC), Forschungszentrum Jülich, D-52425 Jülich, Germany.
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Flesia S, Gaunt DS, Soteros CE, Whittington SG. General model for collapse in lattice animals. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/19/007] [Citation(s) in RCA: 25] [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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15
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Kumar S, Singh Y, Dhar D. Surface adsorption of a self-avoiding polymer chain on a family of finitely ramified fractals. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/26/19/017] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [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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21
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Seno F, Vanderzande C. Non-universality in the collapse of two-dimensional branched polymers. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/27/17/015] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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22
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Flesia S, Gaunt DS, Soteros CE, Whittington SG. Statistics of collapsing lattice animals. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/27/17/016] [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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23
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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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Manna SS, Dhar D. Fractal dimension of backbone of Eden trees. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:R3063-R3066. [PMID: 9965613 DOI: 10.1103/physreve.54.r3063] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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26
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Henkel M, Seno F. Phase diagram of branched polymer collapse. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:3662-3672. [PMID: 9964676 DOI: 10.1103/physreve.53.3662] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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27
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Miljkovic V, Milosevic S, Zivic I. Continuously varying crossover exponent for adsorption of linear polymers on fractals. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:6314-6320. [PMID: 9964149 DOI: 10.1103/physreve.52.6314] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Stella AL. Vesicle model of linear- and branched-polymer theta collapses. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 50:3259-3262. [PMID: 9962376 DOI: 10.1103/physreve.50.3259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Abstract
What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is side-chain "freezing" or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.
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Affiliation(s)
- S Bromberg
- Department of Pharmaceutical Chemistry, University of California, San Francisco 94143-1204
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Serra P, Stilck JF. Polymer model with annealed dilution on the square lattice: A transfer-matrix study. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1994; 49:1336-1343. [PMID: 9961343 DOI: 10.1103/physreve.49.1336] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Orlandini E, Stella AL, Tesi MC, Sullivan F. Vesicle adsorption on a plane: Scaling regimes and crossover phenomena. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:R4203-R4206. [PMID: 9961188 DOI: 10.1103/physreve.48.r4203] [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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Vanderzande C. Vesicles, the tricritical-0-state Potts model, and the collapse of branched polymers. PHYSICAL REVIEW LETTERS 1993; 70:3595-3598. [PMID: 10053914 DOI: 10.1103/physrevlett.70.3595] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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34
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Tuthill GF, Schwalm WA. Biased interacting self-avoiding walks on the four-simplex lattice. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:13722-13734. [PMID: 10003429 DOI: 10.1103/physrevb.46.13722] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Nemirovsky AM, Dudowicz J, Freed KF. Dense self-interacting lattice trees with specified topologies: From light to dense branching. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:7111-7127. [PMID: 9906784 DOI: 10.1103/physreva.45.7111] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kneevic D, Kneevic M, Miloevic S. Critical behavior of an interacting polymer chain in a porous model system: Exact results for truncated simplex lattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:574-585. [PMID: 10001095 DOI: 10.1103/physrevb.45.574] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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37
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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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Meirovitch H, Lim HA. Computer simulation study of the θ‐point in three dimensions. I. Self‐avoiding walks on a simple cubic lattice. J Chem Phys 1990. [DOI: 10.1063/1.458548] [Citation(s) in RCA: 57] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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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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Stella AL, Vanderzande C. Scaling and fractal dimension of Ising clusters at the d=2 critical point. PHYSICAL REVIEW LETTERS 1989; 62:1067-1070. [PMID: 10039568 DOI: 10.1103/physrevlett.62.1067] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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41
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Bouchaud E, Vannimenus J. Polymer adsorption : bounds on the cross-over exponent and exact results for simple models. ACTA ACUST UNITED AC 1989. [DOI: 10.1051/jphys:0198900500190293100] [Citation(s) in RCA: 53] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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42
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Chang IS, Shapir Y. Collapse transition of branched polymers with a tunable number of loops. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:6736-6740. [PMID: 9945351 DOI: 10.1103/physrevb.38.6736] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Lim HA, Guha A, Shapir Y. Tricritical behavior of polymers with loops. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 38:3710-3720. [PMID: 9900810 DOI: 10.1103/physreva.38.3710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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44
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Lam PM. Scaling analysis of the collapse of branched polymers. PHYSICAL REVIEW. B, CONDENSED MATTER 1988; 38:2813-2815. [PMID: 9946595 DOI: 10.1103/physrevb.38.2813] [Citation(s) in RCA: 25] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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45
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Poole PH, Coniglio A, Jan N, Stanley HE. Universality classes for the FTHETA and FTHETA' points. PHYSICAL REVIEW LETTERS 1988; 60:1203. [PMID: 10037969 DOI: 10.1103/physrevlett.60.1203] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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46
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Lam PM. Specific heat and collapse transition of branched polymers. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 36:6988-6992. [PMID: 9942421 DOI: 10.1103/physrevb.36.6988] [Citation(s) in RCA: 34] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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47
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Kneevic M, Vannimenus J. Branched polymers on fractal lattices. PHYSICAL REVIEW. B, CONDENSED MATTER 1987; 35:4988-4997. [PMID: 9940679 DOI: 10.1103/physrevb.35.4988] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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48
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Bartelt NC, Einstein TL, Roelofs LD. Transfer-matrix approach to estimating coverage discontinuities and multicritical-point positions in two-dimensional lattice-gas phase diagrams. PHYSICAL REVIEW. B, CONDENSED MATTER 1986; 34:1616-1623. [PMID: 9939809 DOI: 10.1103/physrevb.34.1616] [Citation(s) in RCA: 52] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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49
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Kneevic M, Vannimenus J. Large-scale properties and collapse transition of branched polymers: Exact results on fractal lattices. PHYSICAL REVIEW LETTERS 1986; 56:1591-1594. [PMID: 10032716 DOI: 10.1103/physrevlett.56.1591] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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50
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Beale PD. Finite-size scaling study of the two-dimensional Blume-Capel model. PHYSICAL REVIEW. B, CONDENSED MATTER 1986; 33:1717-1720. [PMID: 9938476 DOI: 10.1103/physrevb.33.1717] [Citation(s) in RCA: 65] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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