A Study of Finite Size Effects and Periodic Boundary Conditions to Simulations of a Novel Theoretical Self‐Consistent Mean‐Field Approach

2019 ◽  
Vol 28 (5) ◽  
pp. 1900023
Author(s):  
Guanda Yang ◽  
Fritjof Nilsson ◽  
Dirk W. Schubert
Keyword(s):  
Boundary Conditions ◽  
Size Effects ◽  
Periodic Boundary ◽  
Mean Field ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Finite Size Effects ◽  
Field Approach ◽  
Self Consistent

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 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

scholarly journals Effect of Bjerrum pairs on electrostatic properties in an electrolyte solution near charged surfaces: A mean-field approach

2021 ◽  
Author(s):  
Jun-Sik Sin
Keyword(s):  
Electrolyte Solution ◽  
Size Effects ◽  
Mean Field ◽  
Finite Size ◽  
Ion Association ◽  
Finite Size Effects ◽  
Field Approach ◽  
Electrostatic Properties ◽  
Charged Surfaces ◽  
Orientational Ordering

In this paper, we investigate the consequences of ion association, coupled with the considerations of finite size effects and orientational ordering of Bjerrum pairs as well as ions and water...

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.

scholarly journals Finite-Size Effects in the φ4 Field and Lattice Theory Above the Upper Critical Dimension

1998 ◽  
Vol 09 (07) ◽  
pp. 1007-1019 ◽  
Author(s):  
X. S. Chen ◽  
V. Dohm
Keyword(s):  
Size Effects ◽  
Lattice Theory ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Critical Dimension ◽  
Spin Systems ◽  
Finite Size Effects ◽  
Upper Critical Dimension ◽  
Universal Properties ◽  
Binder Cumulant

We demonstrate that the standard O(n) symmetric φ4 field theory does not correctly describe the leading finite-size effects near the critical point of spin systems with periodic boundary conditions on a d-dimensional lattice with d>4. We show that these finite-size effects require a description in terms of a lattice Hamiltonian. For n →∞ and n=1, explicit results are given for the susceptibility and for the Binder cumulant. They imply that these quantities do not have the universal properties predicted previously and that recent analyses of Monte Carlo results for the five-dimensional Ising model are not conclusive.

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