Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions

1996 ◽  
Vol 53 (4) ◽  
pp. 1814-1832 ◽  
Author(s):  
Louisa M. Fraser ◽  
W. M. C. Foulkes ◽  
G. Rajagopal ◽  
R. J. Needs ◽  
S. D. Kenny ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Size Effects ◽  
Quantum Monte Carlo ◽  
Periodic Boundary ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Coulomb Interactions ◽  
Finite Size Effects ◽  
Monte Carlo Calculations

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.

scholarly journals Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids

2016 ◽  
Vol 94 (3) ◽  
Author(s):  
Markus Holzmann ◽  
Raymond C. Clay ◽  
Miguel A. Morales ◽  
Norm M. Tubman ◽  
David M. Ceperley ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Size Effects ◽  
Quantum Monte Carlo ◽  
Finite Size ◽  
Finite Size Effects ◽  
Monte Carlo Calculations

scholarly journals Transient hydrodynamic finite-size effects in simulations under periodic boundary conditions

2017 ◽  
Vol 95 (6) ◽  
Author(s):  
Adelchi J. Asta ◽  
Maximilien Levesque ◽  
Rodolphe Vuilleumier ◽  
Benjamin Rotenberg
Keyword(s):  
Boundary Conditions ◽  
Size Effects ◽  
Periodic Boundary ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Finite Size Effects

Finite-size effects in field theory. Scaling behaviour

2021 ◽  
pp. 760-785
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Finite Volume ◽  
Size Effects ◽  
Short Range ◽  
Periodic Boundary ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Vector Model ◽  
Finite Size Effects ◽  
Infinite Systems ◽  
New Situation

A number of numerical calculations, like Monte Carlo or transfer matrix calculations, are performed with systems in which the size in several or all dimensions is finite. To extrapolate the results to the infinite system, it is thus necessary to understand how the infinite size limit is reached. In particular in a system in which the forces are short range, no phase transition can occur in a finite volume, or in a geometry in which the size is infinite only in one dimension. This indicates that the infinite-size extrapolation is somewhat non-trivial. In this chapter, the problem is analysed in the case of second-order phase transitions, in the framework of the N-vector model. The existence of a finite-size scaling is established, extending renormalization group (RG) arguments to this new situation. Then, finite volume geometry and cylindrical geometry, in which the size is finite in all dimensions except one, are distinguished. It is explained how to adapt the methods used in the case of infinite systems to calculate the new universal quantities appearing in finite-size effects, for example, in d = 4−ϵ or d = 2+ϵ dimensions. Special properties of the commonly used periodic boundary conditions are emphasized.

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