Finite lattice approximation of infinite lattice systems with delays and non-Lipschitz nonlinearities

2018 ◽  
Vol 106 (3-4) ◽  
pp. 169-203 ◽  
Author(s):  
Yejuan Wang ◽  
Meiyu Sui
Keyword(s):  
Finite Lattice ◽  
Lattice Systems ◽  
Infinite Lattice ◽  
Lattice Approximation

Finite lattice systems with true critical behavior

1992 ◽  
Vol 46 (4) ◽  
pp. 1643-1657 ◽  
Author(s):  
J. L. deLyra ◽  
S. K. Foong ◽  
T. E. Gallivan
Keyword(s):  
Critical Behavior ◽  
Finite Lattice ◽  
Lattice Systems

The absorption of ?-radiation in infinite lattice systems

1963 ◽  
Vol 13 (6) ◽  
pp. 1199-1202
Author(s):  
B. M. Terent'ev ◽  
V. A. �l'tekov ◽  
Yu. S. Ryabukhin
Keyword(s):  
Lattice Systems ◽  
Infinite Lattice

scholarly journals ON A MEAN FIELD APPROXIMATION FOR HIGGS-YUKAWA SYSTEMS

1994 ◽  
Vol 09 (11) ◽  
pp. 983-991 ◽  
Author(s):  
SERGEI V. ZENKIN
Keyword(s):  
Phase Diagram ◽  
Phase Structure ◽  
Finite Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Ladder Approximation ◽  
Mean Field Approximation ◽  
Ferromagnetic Phase ◽  
Time Dimension ◽  
Infinite Lattice

We discuss the phase structure of a lattice Higgs-Yukawa system in the variational mean field approximation with contributions of fermionic determinant being calculated in a ladder approximation. In particular, we demonstrate that in this approximation the ferromagnetic phase in the Z2 model with naive fermions can appear as an artifact of a finite lattice and that the phase diagram for this model on infinite lattice changes qualitatively at space-time dimension D = 4 compared with those at D > 4.

THE EFFECT OF THE INCREASE OF LINEAR DIMENSIONS ON EXPONENTS OBTAINED BY FINITE-SIZE SCALING RELATIONS FOR THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

2008 ◽  
Vol 22 (13) ◽  
pp. 1329-1341 ◽  
Author(s):  
G. MÜLAZIMOGLU ◽  
A. DURAN ◽  
Z. MERDAN ◽  
A. GUNEN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Finite Lattice ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton using finite-size lattices with linear dimension 4 ≤ L ≤ 22. The exponents in the finite-size scaling relations for the order parameter, the magnetic susceptibility at the finite-lattice critical temperature and the specific heat at the infinite-lattice critical temperature are computed to be β = 0.5072(58), γ = 1.0287(56) and α = -0.096(17), respectively, which are consistent with the renormalization group prediction of β = 0.5, γ = 1 and α = 0. The critical temperatures for the infinite lattice are found to be [Formula: see text] and [Formula: see text], which are also consistent with the precise results.

Obtaining sharp critical behavior in finite lattice systems

1992 ◽  
Vol 26 ◽  
pp. 601-603
Author(s):  
J.L. deLyra ◽  
S.K. Foong ◽  
T.E. Gallivan
Keyword(s):  
Critical Behavior ◽  
Finite Lattice ◽  
Lattice Systems

Dynamic behavior of stochastic p-Laplacian-type lattice equations

2016 ◽  
Vol 17 (05) ◽  
pp. 1750040 ◽  
Author(s):  
Anhui Gu ◽  
Yangrong Li
Keyword(s):  
Dynamic Behavior ◽  
Multiplicative Noise ◽  
Finite Lattice ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Infinite Lattice ◽  
Lower Semi ◽  
The Family ◽  
Random Attractors ◽  
Type Lattice

In this paper, we consider the dynamic behavior of stochastic [Formula: see text]-Laplacian-type lattice equations perturbed by a multiplicative noise. Under weaker dissipative conditions compared to the cases of stochastic [Formula: see text]-Laplacian-type equations in bounded and unbounded domains, we first obtain the existence of a unique random attractor. We also establish the approximation of the random attractors from finite lattice to infinite lattice, which indicates that the family of random attractors is upper and lower semi-continuous when the number of the lattice nodes tends to infinity.

scholarly journals Cluster-Bethe-Lattice Model for Infinite Lattice Systems

1993 ◽  
Vol 9 (04) ◽  
pp. 473-477
Author(s):  
Zhu Hong-Yao ◽  
◽  
Jiang Yuan-Sheng
Keyword(s):  
Lattice Model ◽  
Bethe Lattice ◽  
Lattice Systems ◽  
Infinite Lattice
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