Finite-size scaling study of the vapor-liquid critical properties of confined fluids: Crossover from three dimensions to two dimensions

2010 ◽  
Vol 132 (14) ◽  
pp. 144107 ◽  
Author(s):  
Yang Liu ◽  
Athanassios Z. Panagiotopoulos ◽  
Pablo G. Debenedetti
Keyword(s):  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Confined Fluids ◽  
Size Scaling ◽  
Vapor Liquid

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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