scholarly journals Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices

1998 ◽  
Vol 57 (1) ◽  
pp. 230-236 ◽  
Author(s):  
Christian D. Lorenz ◽  
Robert M. Ziff
Keyword(s):  
Finite Size ◽  
Precise Determination ◽  
Bond Percolation ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Percolation Thresholds

scholarly journals An analysis of systematic effects in finite size scaling studies using the gradient flow

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Alessandro Nada ◽  
Alberto Ramos
Keyword(s):  
Gauge Theory ◽  
Finite Size ◽  
Gradient Flow ◽  
Flow Time ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Pure Gauge ◽  
Pure Gauge Theory ◽  
Systematic Effects

AbstractWe propose a new strategy for the determination of the step scaling function $$\sigma (u)$$ σ ( u ) in finite size scaling studies using the gradient flow. In this approach the determination of $$\sigma (u)$$ σ ( u ) is broken in two pieces: a change of the flow time at fixed physical size, and a change of the size of the system at fixed flow time. Using both perturbative arguments and a set of simulations in the pure gauge theory we show that this approach leads to a better control over the continuum extrapolations. Following this new proposal we determine the running coupling at high energies in the pure gauge theory and re-examine the determination of the $$\Lambda $$ Λ -parameter, with special care on the perturbative truncation uncertainties.

scholarly journals FINITE-SIZE SCALING IN TWO-DIMENSIONAL CONTINUUM PERCOLATION MODELS

1999 ◽  
Vol 13 (17) ◽  
pp. 577-583 ◽  
Author(s):  
VAN LIEN NGUYEN ◽  
ENRIQUE CANESSA
Keyword(s):  
Finite Size ◽  
Model Systems ◽  
System Structure ◽  
Positive Sign ◽  
Continuum Percolation ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Percolation Parameter ◽  
Percolation Thresholds

We test the universal finite-size scaling of the cluster mass order parameter in two-dimensional (2D) isotropic and directed continuum percolation models below the percolation threshold by computer simulations. We found that the simulation data in the 2D continuum models obey the same scaling expression of mass M to sample size L as generally accepted for isotropic lattice problems, but with a positive sign of the slope in the ln–ln plot of M versus L. Another interesting aspect of the finite-size 2D models is also suggested by plotting the normalized mass in 2D continuum and lattice bond percolation models versus an effective percolation parameter, independent of the system structure (i.e., lattice or continuum) and of the possible directions allowed for percolation (i.e., isotropic or directed) in regions close to the percolation thresholds. Our study is the first attempt to map the scaling behavior of the mass for both lattice and continuum model systems into one curve.

scholarly journals FINITE-SIZE SCALING AND DECONFINEMENT TRANSITION: THE CASE OF 4D SU(2) PURE GAUGE THEORY

2004 ◽  
Vol 19 (19) ◽  
pp. 3209-3216 ◽  
Author(s):  
ALESSANDRO PAPA ◽  
CARLO VENA
Keyword(s):  
Gauge Theory ◽  
Accurate Determination ◽  
Finite Size ◽  
Critical Index ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Pure Gauge ◽  
Simple Lattice ◽  
Pure Gauge Theory

A recently introduced method for determining the critical indices of the deconfinement transition in gauge theories, already tested for the case of 3D SU (3) pure gauge theory, is applied here to 4D SU (2) pure gauge theory. The method is inspired by universality and based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We obtain an accurate determination of the critical index ν, in agreement with the prediction of the Svetitsky–Yaffe conjecture.

scholarly journals A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

2003 ◽  
Vol 14 (07) ◽  
pp. 945-954 ◽  
Author(s):  
MEHMET DİLAVER ◽  
SEMRA GÜNDÜÇ ◽  
MERAL AYDIN ◽  
YİĞİT GÜNDÜÇ
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Taylor Series Expansion ◽  
Scaling Behavior ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
New Approach ◽  
Size Scaling ◽  
Dynamic Exponent ◽  
Good Agreement

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

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