scholarly journals Finite size effects in critical fiber networks

Soft Matter ◽  
2020 ◽  
Vol 16 (29) ◽  
pp. 6784-6793
Author(s):  
Sadjad Arzash ◽  
Jordan L. Shivers ◽  
Fred C. MacKintosh
Keyword(s):  
Phase Transition ◽  
Shear Strain ◽  
Size Effects ◽  
Finite Size ◽  
Scaling Behavior ◽  
Finite Size Scaling ◽  
Finite Size Effects ◽  
Fiber Networks ◽  
Size Scaling ◽  
Mechanical Transition

When subjected to shear strain, underconstrained spring networks undergo a floppy to rigid phase transition. We study the finite-size scaling behavior of this mechanical transition.

Finite-Size Effects and Finite-Size Scaling in Time Evolution During a Colorless Confining Phase Transition

2021 ◽  
Author(s):  
Salah Cherif ◽  
Madjid Lakhdar Hamou Ladrem ◽  
Zainab Zaki Mohammed Alfull ◽  
Rana Meshal Alharbi ◽  
M. A. A. Ahmed
Keyword(s):  
Phase Transition ◽  
Time Evolution ◽  
Size Effects ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Finite Size Effects ◽  
Size Scaling

scholarly journals Lattice φ4 Theory of Finite-Size Effects Above the Upper Critical Dimension

1998 ◽  
Vol 09 (07) ◽  
pp. 1073-1105 ◽  
Author(s):  
X. S. Chen ◽  
V. Dohm
Keyword(s):  
Field Theory ◽  
Lattice Model ◽  
Size Effects ◽  
Lattice Theory ◽  
Finite Size ◽  
Model Parameters ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Finite Size Effects ◽  
Size Scaling

We present a perturbative calculation of finite-size effects near Tc of the φ4 lattice model in a d-dimensional cubic geometry of size L with periodic boundary conditions for d>4. The structural differences between the φ4 lattice theory and the φ4 field theory found previously in the spherical limit are shown to exist also for a finite number of components of the order parameter. The two-variable finite-size scaling functions of the field theory are nonuniversal whereas those of the lattice theory are independent of the nonuniversal model parameters. One-loop results for finite-size scaling functions are derived. Their structure disagrees with the single-variable scaling form of the lowest-mode approximation for any finite ξ/L where ξ is the bulk correlation length. At Tc, the large-L behavior becomes lowest-mode like for the lattice model but not for the field-theoretic model. Characteristic temperatures close to Tc of the lattice model, such as T max (L) of the maximum of the susceptibility χ, are found to scale asymptotically as Tc-T max (L) ~L-d/2, in agreement with previous Monte Carlo (MC) data for the five-dimensional Ising model. We also predict χ max ~Ld/2 asymptotically. On a quantitative level, the asymptotic amplitudes of this large-L behavior close to Tc have not been observed in previous MC simulations at d=5 because of nonnegligible finite-size terms ~L(4-d)/2 caused by the inhomogeneous modes. These terms identify the possible origin of a significant discrepancy between the lowest-mode approximation and previous MC data. MC data of larger systems would be desirable for testing the magnitude of the L(4-d)/2 and L4-d terms predicted by our theory.

scholarly journals True scale-free networks hidden by finite size effects

2020 ◽  
Vol 118 (2) ◽  
pp. e2013825118
Author(s):  
Matteo Serafino ◽  
Giulio Cimini ◽  
Amos Maritan ◽  
Andrea Rinaldo ◽  
Samir Suweis ◽  
...  
Keyword(s):  
Power Law ◽  
Size Effects ◽  
Finite Size ◽  
Statistical Testing ◽  
Finite Size Scaling ◽  
Finite Size Effects ◽  
Scale Free ◽  
Size Scaling ◽  
Naturally Occurring ◽  
Scaling Hypothesis

We analyze about 200 naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees. Specifically, we analyze by finite size scaling analysis the datasets of real networks to check whether the purported departures from power law behavior are due to the finiteness of sample size. We find that a large number of the networks follows a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially involving infrastructure and transportation but also in social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite size effects due to the nature of the sample data.

FINITE-SIZE SCALING AT CRITICAL POINTS WITH SPATIAL ANISOTROPIES

1992 ◽  
Vol 03 (02) ◽  
pp. 367-383 ◽  
Author(s):  
KWAN-TAI LEUNG
Keyword(s):  
Size Effects ◽  
Lattice Gas ◽  
Finite Size ◽  
Nonequilibrium Systems ◽  
Finite Size Scaling ◽  
Nonequilibrium Phase Transition ◽  
Finite Size Effects ◽  
Correlation Lengths ◽  
Size Scaling ◽  
Recent Developments

We report some selected recent developments in the finite-size scaling theory of critical phenomena occurring in systems with strong spatial anisotropies. Such systems are characterized by correlation lengths divergent with different exponents (ν⊥, ν||) along different directions. Attention is focused on the driven diffusive lattice gas that exhibits a second order nonequilibrium phase transition. We present in detail the phenomenology and its comparison with computer simulation. Novel features of finite-size effects in anisotropic nonequilibrium systems are emphasized.

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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