scholarly journals Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions

2003 ◽  
Vol 67 (5) ◽  
Author(s):  
X. S. Chen ◽  
V. Dohm
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Size Effects ◽  
Finite Size ◽  
Spherical Model ◽  
Finite Size Effects ◽  
Free Boundary Conditions ◽  
Mean Spherical Model ◽  
The Mean

scholarly journals TESTING BOUNDARY CONDITIONS EFFICIENCY IN SIMULATIONS OF LONG-RANGE INTERACTING MAGNETIC MODELS

2004 ◽  
Vol 15 (01) ◽  
pp. 115-127 ◽  
Author(s):  
SERGIO A. CANNAS ◽  
CINTIA M. LAPILLI ◽  
DANIEL A. STARIOLO
Keyword(s):  
Low Temperature ◽  
Boundary Conditions ◽  
Size Effects ◽  
Periodic Boundary ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Ferromagnetic Phase ◽  
Temperature Phase ◽  
Finite Size Effects ◽  
Magnetic Systems

Periodic boundary conditions have no unique implementation in magnetic systems where all spins interact with each other through a power law decaying interaction of the form 1/rα, r being the distance between spins. In this work we present a comparative study of the finite size effects oberved in numerical simulations by using first image and infinite image periodic boundary conditions in one- and two-dimensional spin systems with those interactions, including the ferromagnetic, anti-ferromagnetic and competitive interaction cases. Our results show no significative differences between the finite size effects produced by both boundary conditions when the low temperature phase has zero global magnetization, and it depends on the ratio α/d for systems with a low temperature ferromagnetic phase. In the last case the first image convention gives more stronger finite size effects than the other when the system enters into the classical regime α/d≤3/2.

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