共查询到10条相似文献,搜索用时 109 毫秒
1.
X.S. Chen V. Dohm 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,10(4):687-703
We reexamine the range of validity of finite-size scaling in the lattice model and the field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of
the theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite
cutoff. For a confined geometry of linear size L with periodic boundary conditions we analyze the approach towards bulk critical behavior as at fixed for where is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On
the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for
both the lattice model and the field theory in the region . The non-scaling effects in the field theory and in the lattice model differ significantly from each other.
Received 5 February 1999 相似文献
2.
3.
H. Chamati D.M. Danchev N.S. Tonchev 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(2):307-316
A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film
geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given.
We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for
the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs
from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is .
Received 3 June 1999 and Received in final form 16 August 1999 相似文献
4.
I.L. Menezes-Sobrinho J.G. Moreira A.T. Bernardes 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(2):313-318
We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel
fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the
catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding
regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic
and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the
percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation.
Received 24 June 1999 相似文献
5.
X.S. Chen V. Dohm D. Stauffer 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,14(4):699-704
Using field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization M for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with
infinite cutoff gives a scaling form of the equation of state where is the reduced temperature, h is the external field and L is the size of system. Below and at the theory predicts a nonmonotonic dependence of f(x,y) with respect to at fixed and a crossover from nonmonotonic to monotonic behaviour when y is further increased. These results are confirmed by MC simulation. The scaling function f(x,y) obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found
for the bulk value at .
Received 20 July 1999 and Received in final form 11 November 1999 相似文献
6.
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
7.
E. Carlon M. Henkel U. Schollwöck 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(1):99-114
The density matrix renormalization group ( DMRG) is applied to some one-dimensional reaction-diffusion models in the vicinity
of and at their critical point. The stochastic time evolution for these models is given in terms of a non-symmetric “quantum
Hamiltonian”, which is diagonalized using the DMRG method for open chains of moderate lengths (up to about 60 sites). The
numerical diagonalization methods for non-symmetric matrices are reviewed. Different choices for an appropriate density matrix
in the non-symmetric DMRG are discussed. Accurate estimates of the steady-state critical points and exponents can then be
found from finite-size scaling through standard finite-lattice extrapolation methods. This is exemplified by studying the
leading relaxation time and the density profiles of diffusion-annihilation and of a branching-fusing model in the directed
percolation universality class.
Received 2 February 1999 相似文献
8.
J.P. Kemp U.H.E. Hansmann Zheng Yu Chen 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(2):371-374
The similarity in the thermodynamic properties of two completely different theoretical models for the helix-coil transition
is examined critically. The first model is an all-atomic representation for a poly-alanine chain, while the second model is
a minimal helix-forming model that contains no system specifics. Key characteristics of the helix-coil transition, in particular,
the effective critical exponents of these two models agree with each other, within a finite-size scaling analysis.
Received 8 December 1999 相似文献
9.
Anomalous scaling in the Zhang model 总被引:2,自引:0,他引:2
R. Pastor-Satorras A. Vespignani 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,18(2):197-200
We apply the moment analysis technique to analyze large scale simulations of the Zhang sandpile model. We find that this model
shows different scaling behavior depending on the update mechanism used. With the standard parallel updating, the Zhang model
violates the finite-size scaling hypothesis, and it also appears to be incompatible with the more general multifractal scaling
form. This makes impossible its affiliation to any one of the known universality classes of sandpile models. With sequential
updating, it shows scaling for the size and area distribution. The introduction of stochasticity into the toppling rules of
the parallel Zhang model leads to a scaling behavior compatible with the Manna universality class.
Received 8 August 2000 and Received in final form 4 October 2000 相似文献
10.
M. Bengrine A. Benyoussef A. El Kenz M. Loulidi F. Mhirech 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,12(1):129-133
A one-dimensional model of a rice-pile is numerically studied for different driving mechanisms. We found that for a sufficiently
large system, there is a sharp transition between the trivial behaviour of a 1D BTW model and self-organized critical (SOC)
behaviour. Depending on the driving mechanism, the self-organized critical rice-pile model belongs to two different universality
classes.
Received 18 December 1998 相似文献