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

scholarly journals Critical Casimir Force inHe4Films: Confirmation of Finite-Size Scaling

2006 ◽  
Vol 97 (7) ◽  
Author(s):  
A. Ganshin ◽  
S. Scheidemantel ◽  
R. Garcia ◽  
M. H. W. Chan
Keyword(s):  
Casimir Force ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling

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.

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.

scholarly journals Entanglement gap, corners, and symmetry breaking

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Vincenzo Alba
Keyword(s):  
Symmetry Breaking ◽  
Critical Point ◽  
Magnetic Order ◽  
Finite Size ◽  
Spherical Model ◽  
Low Energy ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Energy Part

We investigate the finite-size scaling of the lowest entanglement gap \delta\xiδξ in the ordered phase of the two-dimensional quantum spherical model (QSM). The entanglement gap decays as \delta\xi=\Omega/\sqrt{L\ln(L)}δξ=Ω/Lln(L). This is in contrast with the purely logarithmic behaviour as \delta\xi=\pi^2/\ln(L)δξ=π2/ln(L) at the critical point. The faster decay in the ordered phase reflects the presence of magnetic order. We analytically determine the constant \OmegaΩ, which depends on the low-energy part of the model dispersion and on the geometry of the bipartition. In particular, we are able to compute the corner contribution to \OmegaΩ, at least for the case of a square corner.

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