Finite-size scaling of O(n) models with singular behaviour

1989 ◽  
Vol 67 (10) ◽  
pp. 952-956 ◽  
Author(s):  
Scott Allen ◽  
R. K. Pathria
Keyword(s):  
Spontaneous Magnetization ◽  
Finite Size ◽  
Spherical Model ◽  
Singular Part ◽  
Continuous Variables ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Transition Formula ◽  
Scaling Hypothesis ◽  
Analytical Verification

The finite-size scaling hypothesis of Privman and Fisher (Phys. Rev. B, 30, 322 (1984)) is applied to systems with O(n) symmetry [Formula: see text], confined to geometry Ld − d′ × ∞d′ (where d and d′ are continuous variables such that 2 < d′ < d < 4) and subjected to periodic boundary conditions. Predictions, involving amplitudes as well as exponents, are made on the singular part of the specific heat c(s), spontaneous magnetization m0, magnetic susceptibility χ0, and correlation length ξ0 in the region of the second-order phase transition [Formula: see text]. Analytical verification of these predictions is carried out in the case of the spherical model of ferromagnetism (n = ∞), which includes evaluation of the shift in the critical temperature of the system.

Proof of the equivalence between double scaling limit and finite-size scaling hypothesis

1994 ◽  
Vol 107 (3) ◽  
pp. 507-510
Author(s):  
A. Peterman ◽  
A. Zichichi
Keyword(s):  
Scaling Limit ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Scaling Hypothesis ◽  
Double Scaling Limit

FINITE-SIZE SCALING FOR THE SPHERICAL MODEL WITH LONG-RANGE INTERACTION

1995 ◽  
Vol 09 (18) ◽  
pp. 1117-1121
Author(s):  
K. NOJIMA
Keyword(s):  
Critical Temperature ◽  
Long Range ◽  
Finite Size ◽  
Spherical Model ◽  
Critical Dimension ◽  
Finite Size Scaling ◽  
Range Interaction ◽  
Upper Critical Dimension ◽  
Size Scaling ◽  
Long Range Interaction

The finite-size scaling property of the correlation length for the spherical model with long-range interaction is examined above the critical temperature. The analysis is performed below the upper critical dimension.

Finite-size scaling of O(n) models with singular behaviour: Magnetization and susceptibility in the presence of an external field

1991 ◽  
Vol 69 (6) ◽  
pp. 753-760 ◽  
Author(s):  
Scott Allen ◽  
R. K. Pathria
Keyword(s):  
Phase Transition ◽  
External Field ◽  
Order Phase Transition ◽  
Finite Size ◽  
Spherical Model ◽  
Complete Agreement ◽  
Continuous Variables ◽  
First Order Phase Transition ◽  
Transition Formula ◽  
First Order Phase

The analysis of a previous study (Allen and Pathria. Can. J. Phys. 67, 952 (1989)) on finite-size effects in systems with O(n) symmetry [Formula: see text], confined to geometry Ld−d′ × ∞d′ (where d and d′ are continuous variables such that 2 < d′ < d < 4) and subjected to periodic boundary conditions, is extended (i) to include the region of first-order phase transition (T < Tc) as well as the region of second-order phase transition [Formula: see text] and (ii) to allow the presence of an external field H > 0. Predictions, involving both amplitudes and exponents, are made on the magnetization m and susceptibility χ in different regimes of the variables T, H, and L. Analytical verification of the predicted results is carried out in the case of the spherical model of ferromagnetism (n = ∞), and complete agreement is found.

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.

Universal amplitudes in finite-size scaling: the antiperiodic 3D spherical model

1992 ◽  
Vol 25 (4) ◽  
pp. L207-L211 ◽  
Author(s):  
M Henkel ◽  
R A Weston
Keyword(s):  
Finite Size ◽  
Spherical Model ◽  
Finite Size Scaling ◽  
Size Scaling

An investigation of finite-size scaling for systems with long-range interaction: The spherical model

1990 ◽  
Vol 59 (5-6) ◽  
pp. 1431-1450 ◽  
Author(s):  
Jordan G. Brankov ◽  
Nicholai S. Tonchev
Keyword(s):  
Long Range ◽  
Finite Size ◽  
Spherical Model ◽  
Finite Size Scaling ◽  
Range Interaction ◽  
Size Scaling ◽  
Long Range Interaction

Finite-size scaling Casimir force function: Exact spherical-model results

1996 ◽  
Vol 53 (3) ◽  
pp. 2104-2109 ◽  
Author(s):  
Daniel Danchev
Keyword(s):  
Casimir Force ◽  
Finite Size ◽  
Spherical Model ◽  
Force Function ◽  
Finite Size Scaling ◽  
Size Scaling
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