Universal finite-size scaling functions for critical systems with tilted boundary conditions

1999 ◽  
Vol 59 (2) ◽  
pp. 1585-1588 ◽  
Author(s):  
Yutaka Okabe ◽  
Kazuhisa Kaneda ◽  
Macoto Kikuchi ◽  
Chin-Kun Hu
Keyword(s):  
Boundary Conditions ◽  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Critical Systems ◽  
Size Scaling

scholarly journals Self-similarity in the classification of finite-size scaling functions for toroidal boundary conditions

2008 ◽  
Vol 77 (1) ◽  
Author(s):  
Tsong-Ming Liaw ◽  
Ming-Chang Huang ◽  
Yu-Pin Luo ◽  
Simon C. Lin ◽  
Yen-Liang Chou ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Self Similarity ◽  
Size Scaling

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

Investigation of the Finite Size Properties of the Ising Model Under Various Boundary Conditions

2020 ◽  
Vol 75 (2) ◽  
pp. 175-182
Author(s):  
Magdy E. Amin ◽  
Mohamed Moubark ◽  
Yasmin Amin
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
Boundary Conditions ◽  
Finite Size ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
The One ◽  
Bulk Case

AbstractThe one-dimensional Ising model with various boundary conditions is considered. Exact expressions for the thermodynamic and magnetic properties of the model using different kinds of boundary conditions [Dirichlet (D), Neumann (N), and a combination of Neumann–Dirichlet (ND)] are presented in the absence (presence) of a magnetic field. The finite-size scaling functions for internal energy, heat capacity, entropy, magnetisation, and magnetic susceptibility are derived and analysed as function of the temperature and the field. We show that the properties of the one-dimensional Ising model is affected by the finite size of the system and the imposed boundary conditions. The thermodynamic limit in which the finite-size functions approach the bulk case is also discussed.

Finite-size scaling for the Bose condensate

1985 ◽  
Vol 63 (3) ◽  
pp. 358-365 ◽  
Author(s):  
Surjit Singh ◽  
R. K. Pathria
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Bose Condensate ◽  
Finite Size ◽  
Dirichlet Boundary Conditions ◽  
Three Dimensions ◽  
Bose System ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Temperature Variable

Following the approach of Barber and Fisher, we formulate a finite-size scaling theory for the Bose condensate. Using bulk results as input, we make a number of predictions for the behaviour of the condensate fraction f0(L, T) in an ideal Bose system confined to a hypercube, of side L, in d dimensions. A comparison is made with analytical results for a system in three dimensions under a variety of boundary conditions. While the standard temperature variable t[= (T – Tc)/Tc] is appropriate in the case of periodic and antiperiodic boundary conditions, the use of a shifted variable t[= t – ε(L), where ε(L) = O(L−1 In L)] is essential in the case of Neumann and Dirichlet boundary conditions. Nonetheless, in each case, the predictions of the scaling formulation are fully borne out. Finally, the formulation is extended (i) to include the so-called surface condensate, and (ii) to cover all temperature down to 0 K.

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