Critical exponents for square lattice trails with a fixed number of vertices of degree 4

2002 ◽  
Vol 35 (44) ◽  
pp. 9273-9307 ◽  
Author(s):  
E W James ◽  
C E Soteros
Keyword(s):  
Critical Exponents ◽  
Fixed Number ◽  
Square Lattice

Fem Based Simulation of Percolation Features of Disordered Heterogeneous Media Elastic Properties

1994 ◽  
Vol 367 ◽  
Author(s):  
S.A. Timan ◽  
V.G. Oshmian
Keyword(s):  
Mechanical Properties ◽  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Heterogeneous Media ◽  
Square Lattice ◽  
Monte Carlo Data ◽  
Disordered System ◽  
Phenomenological Renormalization

AbstractThe mechanical properties of the 2D elastic rigid-nonrigid disordered system in dependence on the concentrations of the rigid phase are studied. The system is constructed on the basis of the square lattice and finite element method (FEM) approximation. The elasticity threshold of the FE system and the critical exponents are detemined by the phenomenological renormalization (PR) of the Monte Carlo data.

scholarly journals Active-absorbing phase transition and small-world behaviour in Ising model on finite addition type networks in two dimensions

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Pratik Mullick ◽  
Parongama Sen
Keyword(s):  
Ising Model ◽  
Small World ◽  
Fixed Number ◽  
Two Dimensions ◽  
Square Lattice ◽  
Rich Phase ◽  
Different Types ◽  
Two Parameters ◽  
Absorbing States ◽  
Absorbing Phase Transition

Abstract We consider the ordering dynamics of the Ising model on a square lattice where an additional fixed number of bonds connect any two sites chosen randomly from a total of $N$ lattice sites. The total number of shortcuts added is controlled by two parameters $p$ and $\alpha$ for fixed $N$. The structural properties of the network are investigated which show that the small-world behaviour is obtained along the line $\alpha=\frac{\ln (N/2p)}{\ln N}$, which separates regions with ultra-small world like behaviour and short-ranged lattice like behaviour. We obtain a rich phase diagram in the $p-\alpha$ plane showing the existence of different types of active and absorbing states to which the Ising model evolves to and their boundaries.

Critical Exponents of SAT in Two Dimensional Square Lattice

1999 ◽  
Vol 15 (09) ◽  
pp. 769-774
Author(s):  
Ding En-Yong ◽  
◽  
Huang Yun ◽  
Zhao De-Lu
Keyword(s):  
Critical Exponents ◽  
Square Lattice ◽  
Two Dimensional

QUANTUM MONTE CARLO STUDY OF SITE-DILUTED HEISENBERG ANTIFERROMAGNET ON A SQUARE LATTICE

1999 ◽  
Vol 10 (08) ◽  
pp. 1399-1407 ◽  
Author(s):  
S. TODO ◽  
K. KATO ◽  
H. TAKAYAMA ◽  
K. HARADA ◽  
N. KAWASHIMA ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Critical Exponents ◽  
Quantum Monte Carlo ◽  
Large Scale ◽  
Critical Concentration ◽  
Monte Carlo Study ◽  
Square Lattice ◽  
Heisenberg Antiferromagnet ◽  
Large Systems ◽  
Time Loop

Ground-state phase transition of site-diluted Heisenberg antiferromagnets on a square lattice is studied. By using the continuous-time loop algorithm, we perform large-scale quantum Monte Carlo simulation on large systems at quite low temperatures. It is found that the critical concentration of magnetic sites is independent of the spin size S, and equal to the classical percolation threshold. However, the existence of quantum fluctuations makes the critical exponents deviate from those of the classical percolation transition. It is found that the transition is not universal, i.e., the critical exponents depend on the spin size S.

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