Comment on ‘‘Universality of finite-size scaling: Role of the boundary conditions’’

1986 ◽  
Vol 57 (26) ◽  
pp. 3296-3296 ◽  
Author(s):  
J. Zinn-Justin
Keyword(s):  
Boundary Conditions ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling

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.

Phase Transitions, Critical Phenomena, and Finite-Size Scaling

2019 ◽  
pp. 111-176
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Critical Phenomena ◽  
Quantum Phase Transitions ◽  
Finite Size ◽  
System Size ◽  
Thermal Fluctuations ◽  
Finite Size Scaling ◽  
Size Scaling

Interacting many-particle systems may undergo phase transitions and exhibit critical phenomena in the limit of infinite system size, while the precursors of these phenomena are studied in the theory of finite-size scaling. After surveying the basic notions of phases, phase diagrams, and phase transitions, this chapter focuses on critical behaviour at a second-order phase transition. The Landau-Ginzburg theory and the concept of scaling prepare readers for an elementary introduction to the concepts of the renormalization group, followed by an introduction into the field of quantum phase transitions where quantum fluctuations take over the role of thermal fluctuations.

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
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