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1.
S.B. Santra 《The European Physical Journal B - Condensed Matter and Complex Systems》2003,33(1):75-82
A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints
is studied numerically on the square lattice. The critical percolation threshold p
c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension
d
f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that
expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular
to it, diverge as p → p
c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments
of the cluster size distribution P
s(p) show power law behaviour with | p - p
c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found
to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality
class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling
relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in
favour of the assumed scaling function form of P
s(p). The results obtained are in good agreement with other model calculations.
Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003
RID="a"
ID="a"e-mail: santra@iitg.ernet.in 相似文献
2.
D. Loison K.D. Schotte 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):735-743
The nature of the phase transition for the XY stacked triangular antiferromagnet (STA) is a controversial subject at present. The field theoretical renormalization group
(RG) in three dimensions predicts a first order transition. This prediction disagrees with Monte-Carlo (MC) simulations which
favor a new universality class or a tricritical transition. We simulate by the Monte-Carlo method two models derived from
the STA by imposing the constraint of local rigidity which should have the same critical behavior as the original model. A
strong first order transition is found. Following Zumbach we analyze the second order transition observed in MC studies as
due to a fixed point in the complex plane. We review the experimental results in order to clarify the critical behavior observed.
Received: 18 February 1998 / Revised: 24 April 1998 / Accepted: 30 April 1998 相似文献
3.
Vazquez A Sotolongo-Costa O 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(1):944-947
The avalanche statistics in a stochastic sandpile model where toppling takes place with a probability p is investigated. The limiting case p=1 corresponds to the Bak-Tang-Wiesenfeld (BTW) model with a deterministic toppling rule. Based on the moment analysis of the distribution of avalanche sizes we conclude that for 0
相似文献
4.
A.K. Hartmann U. Nowak 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(1):105-109
We investigate the critical behavior of three-dimensional random-field Ising systems with both Gauss and bimodal distribution
of random fields and additional the three-dimensional diluted Ising antiferromagnet in an external field. These models are
expected to be in the same universality class. We use exact ground-state calculations with an integer optimization algorithm
and by a finite-size scaling analysis we calculate the critical exponents , , and . While the random-field model with Gauss distribution of random fields and the diluted antiferromagnet appear to be in same
universality class, the critical exponents of the random-field model with bimodal distribution of random fields seem to be
significantly different.
Received: 9 July 1998 / Received in final form: 15 July 1998 / Accepted: 20 July
1998 相似文献
5.
P. Bhattacharyya 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(2):247-252
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by Monte Carlo simulation near a critical
point which marks a second-order phase transition from an active state to an effectively unique absorbing state. Values obtained
for the dynamic critical exponents indicate that the transition belongs to the universality class of directed percolation.
Finally the model is compared with a previously studied one to show that a difference in the nature of the absorbing states
places them in different universality classes.
Received: 6 February 1998 / Revised and Accepted: 17 February 1998 相似文献
6.
H. Hinrichsen M. Howard 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,7(4):635-643
We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the
spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for
long-range infections which decays in d spatial dimensions as . Extensive numerical simulations are performed in order to determine the density exponent and the correlation length exponents and for various values of . We observe that these exponents vary continuously with , in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with
algebraically distributed long-range interactions.
Received: 4 September 1998 / Accepted: 22 September 1998 相似文献
7.
E.L. Præstgaard B. Schmittmann R.K.P. Zia 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,18(4):675-695
We investigate the collective behavior of an Ising lattice gas, driven to non-equilibrium steady states by being coupled to
two thermal baths. Monte Carlo methods are applied to a two-dimensional system in which one of the baths is fixed at infinite
temperature. Both generic long range correlations in the disordered state and critical properties near the second order transition
are measured. Anisotropic scaling, a key feature near criticality, is used to extract and some critical exponents. On the theoretical front, a continuum theory, in the spirit of Landau-Ginzburg, is presented.
Being a renormalizable theory, its predictions can be computed by standard methods of -expansions and found to be consistent with simulation data. In particular, the critical behavior of this system belongs to
a universality class which is quite different from the uniformly driven Ising model.
Received 4 October 2000 相似文献
8.
K.J. Wiese 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,1(3):269-272
The dynamical scaling properties of selfavoiding polymerized membranes with internal dimension D are studied using model A dynamics. It is shown that the theory is renormalizable to all orders in perturbation theory and
that the dynamical scaling exponent z is given by . This result applies especially to membranes (D=2) but also to polymers (D=1).
Received: 5 September 1997 / Accepted: 17 November 1997 相似文献
9.
T. Schneider J. Hofer M. Willemin J.M. Singer H. Keller 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(4):413-416
Anisotropic Ginzburg-Landau superconductors of extreme type-II are considered in an approximation where magnetic field fluctuations
are neglected. A formulation of the scaling properties is presented for the singular part of the free energy density in the
presence of a magnetic field. From the existence of a magnetization, a diamagnetic susceptibility and superconductivity we
determine the limiting behavior of the scaling function in the vicinity of the zero field transition temperature, where critical
fluctuations dominate. Our predictions for the temperature and field dependence of magnetization, magnetic torque and melting
line etc., uncover the universal critical properties and provide an extension of hitherto used mean-field treatments. The results are
consistent with experimental data.
Received: 24 April 1998 / Accepted: 5 May 1998 相似文献
10.
T. Emig T. Nattermann 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,8(4):525-546
The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects
is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds,
e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder
driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough
state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly,
by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature
dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects
relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p
c
the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models.
Received 28 August 1998 相似文献
11.
S. Lübeck 《Journal of statistical physics》2006,123(1):193-221
We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations.
PACS numbers: 05.70.Ln, 05.50.+q, 05.65.+b 相似文献
12.
We analyze a controversial topic about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both theoretical and numerical studies agree on the validity of the extended Harris criterion [A. Weinrib, B.I. Halperin, Phys. Rev. B 27 (1983) 413] and indicate the existence of a new universality class, numerical values of the critical exponents found so far differ considerably. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising model with non-magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice. The Swendsen-Wang algorithm is used alongside with a histogram reweighting technique and finite-size scaling analysis to evaluate the values of critical exponents governing magnetic phase transition. Our estimates for these exponents differ from both previous numerical simulations and are in favor of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlation decay. 相似文献
13.
Through using the methods of
finite-size effect and short time dynamic scaling, we study the critical
behavior of parasitic disease spreading process in a diffusive population
mediated by a static vector environment. Through comprehensive analysis of
parasitic disease spreading we find that this model presents a dynamical
phase transition from disease-free state to endemic state with a finite
population density. We determine the critical population density, above which
the system reaches an epidemic spreading stationary state. We also perform a
scaling analysis to determine the order parameter and critical relaxation
exponents. The results show that the model does not belong to the usual
directed percolation universality class and is compatible with the class of
directed percolation with diffusive and conserved
fields. 相似文献
14.
We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second-order
phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a macroscopic end-to-end
distance at high forces. At low temperatures, the sequence inhomogeneities modify the critical behaviour. We provide numerical
evidence for the universality of the critical exponents which, by extrapolation of the scaling laws to zero force, contain
useful information on the ground-state (f = 0) properties. This provides a good method for quantitative studies of scaling exponents characterizing the collapsed globule.
In order to get rid of the blurring effect of thermal fluctuations, we restrict ourselves to the ground state at fixed external
force. We analyze the statistics of rearrangements, in particular below the critical force, and point out its implications
for force-extension experiments on single molecules.
Received 18 June 2002 and Received in final form 23 September 2002
RID="a"
ID="a"e-mail: muller@ipno.in2p3.fr 相似文献
15.
A nanosecond scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as
it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents γ and
β are found to be 1.7±0.1 and 0.41±0.01 in agreement with the best percolation results in three dimensions.
Received 29 August 2002
RID="a"
ID="a"e-mail: erzan@gursey.gov.tr e-mail: erzan@itu.edu.tr 相似文献
16.
Jihui Han Wei Li Zhu Su Webing Deng 《The European Physical Journal B - Condensed Matter and Complex Systems》2017,90(11):220
In this paper we present our study on the critical behavior of a stochastic anisotropic Bak–Sneppen (saBS) model, in which a parameter α is introduced to describe the interaction strength among nearest species. We estimate the threshold fitness f c and the critical exponent τ r by numerically integrating a master equation for the distribution of avalanche spatial sizes. Other critical exponents are then evaluated from previously known scaling relations. The numerical results are in good agreement with the counterparts yielded by the Monte Carlo simulations. Our results indicate that all saBS models with nonzero interaction strength exhibit self-organized criticality, and fall into the same universality class, by sharing the universal critical exponents. 相似文献
17.
P. E. Theodorakis N. G. Fytas 《The European Physical Journal B - Condensed Matter and Complex Systems》2011,81(2):245-251
We implement a two-stage approach of the Wang-Landau algorithm to investigate the critical properties of the 3D Ising
model with quenched bond randomness. In particular, we consider the case where disorder couples to the nearest-neighbor
ferromagnetic interaction, in terms of a bimodal distribution of strong versus weak bonds. Our simulations are carried out
for
large ensembles of disorder realizations and lattices with linear sizes L in the range L=8-64L=8{-}64. We apply well-established
finite-size scaling techniques and concepts from the scaling theory of disordered systems to describe the nature of the phase
transition of the disordered model, departing gradually from the fixed point of the pure system. Our analysis (based on the
determination of the critical exponents) shows that the 3D random-bond Ising model belongs to the same universality class
with the site- and bond-dilution models, providing a single
universality class for the 3D Ising model with these three types of quenched uncorrelated disorder. 相似文献
18.
We numerically investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on directed small-world networks. We find that the avalanche size and duration distribution follow a power law for all rewiring probabilities p. Specially, we find that, approaching the thermodynamic limit (L→∞), the values of critical exponents do not depend on p and are consistent with the mean-field solution in Euclidean space for any p>0. In addition, we measure the dynamic exponent in the relation between avalanche size and avalanche duration and find that the values of the dynamic exponents are also consistent with the mean-field values for any p>0. 相似文献
19.
M.I. Marqués J.A. Gonzalo 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(2):317-321
The Monte Carlo (MC) approach is used to check the validity of the scaling relationship for the effective critical exponents in thin Ising films. We investigate this relationship not just in the critical region
but throughout the crossover to the expected two-dimensional behavior. Our results indicate that this scaling relationship
is very well-fulfilled throughout the entire crossover temperature region, as predicted by a previous renormalization group
analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for plates with increasing L, up to L=100. The evolution of the maximum value of the effective critical exponents with film thickness is discussed.
Received 22 April 1999 相似文献