共查询到20条相似文献,搜索用时 15 毫秒
1.
Marco Gherardi 《Journal of statistical physics》2009,136(5):864-874
We numerically test the correspondence between the scaling limit of self-avoiding walks (SAW) in the plane and Schramm-Loewner
evolution (SLE) with κ=8/3. We introduce a discrete-time process approximating SLE in the exterior of a small disc and compare the distribution
functions for an internal point in the SAW and a point at a fixed fractal variation on the SLE, finding good agreement. This
provides numerical evidence in favor of a conjecture by Lawler, Schramm and Werner. The algorithm turns out to be an efficient
way of computing the position of an internal point in the SAW. 相似文献
2.
Tom Kennedy 《Journal of statistical physics》2004,114(1-2):51-78
Simulations of the two-dimensional self-avoiding walk (SAW) are performed in a half-plane and a cut-plane (the complex plane with the positive real axis removed) using the pivot algorithm. We test the conjecture of Lawler, Schramm, and Werner that the scaling limit of the two-dimensional SAW is given by Schramm's stochastic Loewner evolution (SLE). The agreement is found to be excellent. The simulations also test the conformal invariance of the SAW since conformal invariance implies that if we map infinite length walks in the cut-plane into the half plane using the conformal map $z \to \sqrt z$ , then the resulting walks will have the same distribution as the SAW in the half plane. The simulations show excellent agreement between the distributions. 相似文献
3.
Tom Kennedy 《Journal of statistical physics》2012,146(2):281-293
We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half
plane and radial SLE8/3 in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power
of the distance to the endpoint of the curve and apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial SLE8/3. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using
the conjectured relationship between the SAW and radial SLE8/3, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few
hundredths of a percent of the conjectured values. 相似文献
4.
Motivated by Kesten’s bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Itô’s excursion decomposition of a Brownian motion according to its zeros. 相似文献
5.
We study the two- and three-dimensional, superrenormalizable Edwards model and the self-avoiding walk model of polymers. Using a Schwinger-Dyson equation and upper and lower bounds on correlations in terms of “skeleton diagrams” [6] we establish the existence of a non-trivial continuum limit in the two- and three-dimensional, superrenormalizable Edwards model. We also prove that perturbation theory is asymptotic for the continuum correlations of these models.A fairly detailed analysis of the approach to the critical point in the self-avoiding walk model is presented. In particular, we show that η<1. In dimension d?4, we discuss rigorous consequences of the conjecture that η is non-negative: among other implications, we derive that the continuum limit is trivial and that γ=1, in d?5 dimensions, and that corrections to mean-field scaling laws are at most logarithmic in four dimensions. 相似文献
6.
We study a model for the backbone of proteins on a square lattice which consists of the path traced out by a self-avoiding walk (SAW) on the lattice and bridges not belonging to sites on the SAW but connecting nearest neighbor sites of the SAW. We calculated the fractal dimensiond
w for random walk on this model and found thatd
w2.6, in disagreement with a recent suggestion thatd
w should be 2. 相似文献
7.
Tom Kennedy 《Journal of statistical physics》2007,128(6):1263-1277
The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm–Loewner evolution (SLE)
for a suitable value of the parameter κ. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization
(with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this
parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support
this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized
curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization. 相似文献
8.
Nathan Clisby 《Journal of statistical physics》2018,172(2):477-492
We study self-avoiding walks on the four-dimensional hypercubic lattice via Monte Carlo simulations of walks with up to one billion steps. We study the expected logarithmic corrections to scaling, and find convincing evidence in support the scaling form predicted by the renormalization group, with an estimate for the power of the logarithmic factor of 0.2516(14), which is consistent with the predicted value of 1/4. We also characterize the behaviour of the pivot algorithm for sampling four dimensional self-avoiding walks, and conjecture that the probability of a pivot move being successful for an N-step walk is \(O([ \log N ]^{-1/4})\). 相似文献
9.
H. L. Bhan V. K. Bhat Y. Singh S. S. Manna 《Zeitschrift für Physik B Condensed Matter》1989,74(3):389-393
Random walk on a self-avoiding walk with superconducting local bridges is studied by Real Space renormalization group technique. We enumerate SAWs in two dimensions for a square lattice by using corner rule and equal averaging method. For a SAW network with superconducting bridges we estimate the exponents for end to end resistance and linear part as 0.8625 and 0.81907 respectively. We also obtain the shortest path exponent =0.9782 by equal averaging technique. 相似文献
10.
The conformation of circular DNA molecules of various lengths adsorbed in a 2D conformation on a mica surface is studied. The results confirm the conjecture that the critical exponent nu is topologically invariant and equal to the self-avoiding walk value (in the present case nu=3/4), and that the topology and dimensionality of the system strongly influence the crossover between the rigid regime and the self-avoiding regime at a scale L approximately 7l{p}. Additionally, the bond correlation function scales with the molecular length L as predicted. For molecular lengths L相似文献
11.
W. M. Koo 《Journal of statistical physics》1995,81(3-4):561-578
Based on transfer matrix techniques and finite-size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact values predicted recently. The polymer is also found to undergo a spiral transition for sufficiently strong attractive interaction. The fractal dimension of the polymer is computed in the repulsive and attractive regimes and at the spiral transition point. The later is found to be different from that at the collapse transition of the ordinary self-avoiding walk. 相似文献
12.
We investigate the approach to the critical point and the scaling limit of a variety of models on a four-dimensional lattice, including g|φ|44 theory and the self-avoiding random walk. Our results, both theoretical and numerical, provide strong evidence for the triviality of the scaling limit and for logarithmic corrections to mean field scaling laws, as predicted by the perturbative renormalization group. We relate logarithmic corrections to scaling to the triviality of the scaling limit. Our numerical analysis is based on a novel, high-precision Monte Carlo technique. 相似文献
13.
Remco van der Hofstad 《Communications in Mathematical Physics》2006,265(3):547-583
We construct a measure valued Markov process which we call infinite canonical super-Brownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian motion is a natural candidate for the scaling limit of various random branching objects on
when these objects are critical, mean-field and infinite. We prove that ICSBM is the scaling limit of the spread-out oriented percolation incipient infinite cluster above 4 dimensions and of incipient infinite branching random walk in any dimension. We conjecture that it also arises as the scaling limit in various other models above the upper-critical dimension, such as the incipient infinite lattice tree above 8 dimensions, the incipient infinite cluster for unoriented percolation above 6 dimensions, uniform spanning trees above 4 dimensions, and invasion percolation above 6 dimensions. 相似文献
14.
The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N-->infinity they are strictly finite in number but their radius of gyration R(c) is power law distributed proportional to R(-tau)(c), where tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging length scales is associated with the R(c) distribution. A possibly superuniversal tau = 2 is also expected for the contacts of a self-avoiding or random walk with a confining wall. 相似文献
15.
A Flory approximant for the exponent describing the end-to-end distance of a self-avoiding walk (SAW) on fractals is derived. The approximant involves the fractal dimensionalities of the backbone and of the minimal path, and the exponent describing the resistance of the fractal. The approximant yields values which are very close to those available from exact and numerical calculations. 相似文献
16.
Bikas K. Chakrabarti 《Physica A》2007,384(1):25-27
We will utilise the self-avoiding walk (SAW) mapping of the vortex line conformations in turbulence to get the Kolmogorov scale dependence of energy dispersion from SAW statistics, and the knowledge of the effects of disordered fractal geometries on the SAW statistics. These will give us the Kolmogorov energy dispersion exponent value for turbulence in porous media in terms of the size exponent for polymers in the same. We argue that the exponent value will be somewhat less than for turbulence in porous media. 相似文献
17.
18.
We study the distribution of the end-to-end distance of continuous-time self-avoiding random walks (CTRW) in dimension four from two viewpoints. From a real-space renormalization-group map on probabilities, we conjecture the asymptotic behavior of the end-to-end distance of a weakly self-avoiding random walk (SARW) that penalizes two-body interactions of random walks in dimension four on a hierarchical lattice. Then we perform the Monte Carlo computer simulations of CTRW on the four-dimensional integer lattice, paying special attention to the difference in statistical behavior of the CTRW compared with the discrete-time random walks. In this framework, we verify the result already predicted by the renormalization-group method and provide new results related to enumeration of self-avoiding random walks and calculation of the mean square end-to-end distance and gyration radius of continous-time self-avoiding random walks. 相似文献
19.
Bertrand Duplantier 《Nuclear Physics B》1994,430(3):489-533
The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a d-dimensional lattice obeys hyperscaling. The combination pNR2Nd/2μ−N (where pN is the number of configurations of an oriented and rooted N-step ring, R2N a typical average size squared, and μ the SAW effective connectivity constant of the lattice) is equal for N å ∞ to a lattice-dependent constant times a universal amplitude A(d). The latter amplitude is calculated directly from the minimal continous Edwards model to second order in 4 − d. The case of rings at the upper critical dimension d = 4 is also studied. The results are checked against field-theoretical calculations, and former simulations. As a consequence, we show that the universal constant λ appearing to second order in in all critical phenomena amplitude ratios is equal to
. 相似文献
20.
Gregory F. Lawler 《Journal of statistical physics》1988,50(1-2):91-108
If(n) is the position of the self-avoiding random walk in
d
obtained by erasing loops from simple random walk, then it is proved that the mean square displacementE(¦(n)¦2) grows at least as fast as the Flory predictions for the usual SAW, i.e., at least as fast asn
3/2 ford=2 andn
6/5 ford=3. In particular, if the mean square displacement of the usual SAW grows liken
1.18... ind=3, as expected, then the loop-erased process is in a different universality class. 相似文献