Symmetry breaking and finite size scaling in antiferromagnets

1993 ◽  
Vol 3 (2) ◽  
pp. 291-298 ◽  
Author(s):  
P. Azaria ◽  
B. Delamotte ◽  
D. Mouhanna
Keyword(s):  
Symmetry Breaking ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling

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.

scholarly journals A NEW APPROACH TO DYNAMIC FINITE-SIZE SCALING

2003 ◽  
Vol 14 (07) ◽  
pp. 945-954 ◽  
Author(s):  
MEHMET DİLAVER ◽  
SEMRA GÜNDÜÇ ◽  
MERAL AYDIN ◽  
YİĞİT GÜNDÜÇ
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Taylor Series Expansion ◽  
Scaling Behavior ◽  
Dynamic Scaling ◽  
Finite Size Scaling ◽  
New Approach ◽  
Size Scaling ◽  
Dynamic Exponent ◽  
Good Agreement

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x0 to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

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