scholarly journals Continuum limits and exact finite-size-scaling functions for one-dimensionalO(N)-invariant spin models

1997 ◽  
Vol 86 (3-4) ◽  
pp. 581-673 ◽  
Author(s):  
Attilio Cucchieri ◽  
Tereza Mendes ◽  
Andrea Pelissetto ◽  
Alan D. Sokal
Keyword(s):  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Spin Models ◽  
Size Scaling

scholarly journals Comparison of finite-size-scaling functions for 3d O(N) spin models to QCD

2002 ◽  
Vol 106-107 ◽  
pp. 498-500 ◽  
Author(s):  
T. Schulze ◽  
J. Engels ◽  
S. Holtmann ◽  
T. Mendes
Keyword(s):  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Spin Models ◽  
Size Scaling

scholarly journals Finite-size-scaling functions for 3d O(4) and O(2) spin models and QCD

2001 ◽  
Vol 514 (3-4) ◽  
pp. 299-308 ◽  
Author(s):  
J. Engels ◽  
S. Holtmann ◽  
T. Mendes ◽  
T. Schulze
Keyword(s):  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Spin Models ◽  
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 UNIVERSAL FINITE-SIZE-SCALING FUNCTIONS

1996 ◽  
Vol 07 (03) ◽  
pp. 287-294 ◽  
Author(s):  
YUTAKA OKABE ◽  
MACOTO KIKUCHI
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Order Parameter ◽  
Finite Size ◽  
Square Lattice ◽  
Parameter Distribution ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Regular Lattices

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document