scholarly journals Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems

2021 ◽  
Vol 2094 (2) ◽  
pp. 022038
Author(s):  
T V Yakunina ◽  
V N Udodov
Keyword(s):  
Critical Exponent ◽  
Percolation Threshold ◽  
Correlation Length ◽  
Adjacency Matrix ◽  
Nearest Neighbors ◽  
Percolation Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One

Abstract A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.

Correlation length of the one-dimensional Bose gas

1985 ◽  
Vol 111 (8-9) ◽  
pp. 419-422 ◽  
Author(s):  
N.M. Bogoliubov ◽  
V.E. Korepin
Keyword(s):  
Correlation Length ◽  
Bose Gas ◽  
One Dimensional ◽  
The One

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Deformation of sliding charge density wave in Rb0.3MoO3

2002 ◽  
Vol 12 (9) ◽  
pp. 323-324
Author(s):  
D. Le Bolloc'h ◽  
S. Ravy ◽  
P. Senzier ◽  
C. Pasquier ◽  
C. Detlefs
Keyword(s):  
Charge Density ◽  
Correlation Length ◽  
Charge Density Wave ◽  
Density Wave ◽  
Relaxation Times ◽  
X Ray Diffraction ◽  
Electrical Field ◽  
One Dimensional ◽  
High Q ◽  
The One

The correlation length of the charge density wave ordering in Rb0.3, MoO, has been studied by x-ray diffraction under electric field applied along the one-dimensional axis. The (10, 0.25, -5.5) satellite reflection has been measured in 3D, using high Q-resolution available at the ESRF. Under electrical field, the satellite reaches two stable positions depending on the temperature. It can switch from one to another as a function of the temperature and the current with very long relaxation times ($\rm 10^{th}$ of minutes). After several cycling with T and E, the satellite reflection is found to shift in the 3 main directions. The width of the satellite is reduced by a factor of two in the k-direction and an increase of the transverse correlation length is observed in the two others: the ordered domains look elongated, reaching until 5000 Å in the direction of the applied field and around 1OOO Å, in the perpendicular directions.

Critical behavior of percolation and Markov fields on branching planes

1993 ◽  
Vol 30 (3) ◽  
pp. 538-547 ◽  
Author(s):  
C. Chris Wu
Keyword(s):  
Continuous Function ◽  
Critical Behavior ◽  
Mean Field ◽  
Percolation Model ◽  
Homogeneous Tree ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Percolation Probability ◽  
Triangle Condition ◽  
Markov Fields

For an independent percolation model on, whereis a homogeneous tree andis a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probabilityθ(p) is a continuous function ofpat the critical pointpc, and the critical exponents,γ,δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields onare also obtained.

Correlation length of the one-dimensional Bose gas

1985 ◽  
Vol 257 ◽  
pp. 766-778 ◽  
Author(s):  
N.M. Bogoliubov ◽  
V.E. Korepin
Keyword(s):  
Correlation Length ◽  
Bose Gas ◽  
One Dimensional ◽  
The One
Sign in / Sign up

Export Citation Format

Share Document