Universality of subleading corrections for self-avoiding walks in the presence of one-dimensional defects

Caracciolo, Sergio; Causo, Maria Serena; Pelissetto, Andrea

doi:10.1088/0305-4470/30/14/009

Cited by 4 publications

(2 citation statements)

References 32 publications

(53 reference statements)

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“…It is interesting to observe the dependence of the critical exponents on the dimensionality and the presence of self-avoidance when the cone/wedge is reduced to a semi-infinite line (when α → π) [26][27][28][29]. In d = 2, a semi-infinite line is a significant barrier to the walk and the change in the critical exponent ∆γ π > 0.…”

Section: Measurement Of ∆γαmentioning

confidence: 99%

“…In d = 2, a semi-infinite line is a significant barrier to the walk and the change in the critical exponent ∆γ π > 0. (In the language of renormalization group, one can say that in this case, the boundary constitutes a relevant perturbation on the free space Hamiltonian [26,29]). In d = 3, the semi-infinite line is not a significant barrier and does not change the critical exponents.…”

Section: Measurement Of ∆γαmentioning

confidence: 99%

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Long polymers near wedges and cones

Hammer

Kantor

2015

Phys. Rev. E

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We perform a Monte Carlo study of N-step self-avoiding walks, attached to the corner of an impenetrable wedge in two dimensions (d=2), or the tip of an impenetrable cone in d=3, of sizes ranging up to N=10(6) steps. We find that the critical exponent γ(α), which determines the dependence of the number of available conformations on N for a cone or wedge with opening angle α, is in good agreement with the theory for d=2. We study the end-point distribution of the walks in the allowed space and find similarities to the known behavior of random walks (ideal polymers) in the same geometry. For example, the ratio between the mean square end-to-end distances of a polymer near the cone or wedge and a polymer in free space depends linearly on γ(α), as is known for ideal polymers. We show that the end-point distribution of polymers attached to a wedge does not separate into a product of angular and radial functions, as it does for ideal polymers in the same geometry. The angular dependence of the end position of polymers near the wedge differs from theoretical predictions.

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Section: Measurement Of ∆γαmentioning

confidence: 99%

Section: Measurement Of ∆γαmentioning

confidence: 99%

Long polymers near wedges and cones

Hammer

Kantor

2015

Phys. Rev. E

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Two-point correlation function of three-dimensionalO(N)models: The critical limit and anisotropy

et al. 1998

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In three-dimensional O(N) models, we investigate the low-momentum behavior of the two-point Green's function G(x) in the critical region of the symmetric phase. We consider physical systems whose criticality is characterized by a rotationally invariant fixed point. Several approaches are exploited, such as strong-coupling expansion of lattice N-vector model, and 1/N expansion, field-theoretical methods within the 4 continuum formulation. Non-Gaussian corrections to the universal low-momentum behavior of G(x) are evaluated, and found to be very small. In nonrotationally invariant physical systems with O(N)-invariant interactions, the vanishing of the spatial anisotropy approaching the rotationally invariant fixed point is described by a critical exponent , which is universal and is related to the leading irrelevant operator breaking rotational invariance. At Nϭϱ one finds ϭ2. We show that, for all values of Nу0, Ӎ2.

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Polymer depletion effects near mesoscopic particles

1999

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The behavior of mesoscopic particles dissolved in a dilute solution of long, flexible, and nonadsorbing polymer chains is studied by field-theoretic methods. For spherical and cylindrical particles the solvation free energy for immersing a single particle in the solution is calculated explicitly. Important features are qualitatively different for self-avoiding polymer chains as compared with ideal chains. The results corroborate the validity of the Helfrich-type curvature expansion for general particle shapes and allow for quantitative experimental tests. For the effective interactions between a small sphere and a wall, between a thin rod and a wall, and between two small spheres, quantitative results are presented. A systematic approach for studying effective many-body interactions is provided. The common Asakura-Oosawa approximation modeling the polymer coils as hard spheres turns out to fail completely for small particles and still fails by about 10% for large particles.

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Universality of subleading corrections for self-avoiding walks in the presence of one-dimensional defects

Cited by 4 publications

References 32 publications

Long polymers near wedges and cones

Long polymers near wedges and cones

Two-point correlation function of three-dimensionalO(N)models: The critical limit and anisotropy

Polymer depletion effects near mesoscopic particles

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