Finite-Size Scaling Analysis of a Three-Dimensional Blume–Capel Model in the Presence of External Magnetic Field

2008 ◽  
Vol 25 (7) ◽  
pp. 2599-2602 ◽  
Author(s):  
H Demirel ◽  
A Özkan ◽  
B Kutlu
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Three Dimensional ◽  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling

RECENT DEVELOPMENTS IN ISING SPIN GLASSES

1996 ◽  
Vol 07 (03) ◽  
pp. 327-335 ◽  
Author(s):  
A. P. YOUNG ◽  
N. KAWASHIMA
Keyword(s):  
Transition Temperature ◽  
Spin Glasses ◽  
Three Dimensional ◽  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Ising Spin ◽  
Recent Developments ◽  
Rule Out

We have studied the three-dimensional Ising spin glass with a ± J distribution by Monte Carlo simulations. Using larger sizes and much better statistics than in earlier work, a finite size scaling analysis shows quite strong evidence for a finite transition temperature, Tc, with ordering below Tc. Our estimate of the transition temperature is rather lower than in earlier work, and the value of the correlation length exponent, ν, is somewhat higher. Because there may be (unknown) corrections to finite size scaling, we do not completely rule out the possibility that Tc = 0 or that Tc is finite but with no order below Tc. However, from our data, these possibilities seem less likely.

scholarly journals Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

2009 ◽  
Vol 80 (2) ◽  
Author(s):  
L. A. Fernandez ◽  
V. Martin-Mayor ◽  
S. Perez-Gaviro ◽  
A. Tarancon ◽  
A. P. Young
Keyword(s):  
Phase Transition ◽  
Spin Glass ◽  
Three Dimensional ◽  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Heisenberg Spin ◽  
Size Scaling

scholarly journals ANISOTROPIC FINITE-SIZE SCALING ANALYSIS OF A THREE-DIMENSIONAL DRIVEN-DIFFUSIVE SYSTEM

1999 ◽  
Vol 10 (05) ◽  
pp. 853-873 ◽  
Author(s):  
KWAN-TAI LEUNG ◽  
JIAN-SHENG WANG
Keyword(s):  
Strong Field ◽  
Three Dimensional ◽  
Finite Size ◽  
Numerical Data ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Scaling Properties ◽  
Size Scaling ◽  
Driven Diffusive System ◽  
Diffusive System

We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumping along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wang's prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.

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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