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Nonequilibrium model on Archimedean lattices

100%
Lima F.
Open Physics
|
2014
|
vol. 12
|
issue 3
185-191
EN
On (4, 6, 12) and (4, 82) Archimedean lattices, the critical properties of the majority-vote model are considered and studied using the Glauber transition rate proposed by Kwak et al. [Kwak et al., Phys. Rev. E, 75, 061110 (2007)] rather than the traditional majority-vote with noise [Oliveira, J. Stat. Phys. 66, 273 (1992)]. We obtain T c and the critical exponents for this Glauber rate from extensive Monte Carlo studies and finite size scaling. The calculated values of the critical temperatures and Binder cumulant are T c = 0.651(3) and U 4* = 0.612(5), and T c = 0.667(2) and U 4* = 0.613(5), for (4, 6, 12) and (4, 82) lattices respectively, while the exponent (ratios) β/ν, γ/ν and 1/ν are respectively: 0.105(8), 1.48(11) and 1.16(5) for (4, 6, 12); and 0.113(2), 1.60(4) and 0.84(6) for (4, 82) lattices. The usual Ising model and the majority-vote model on previously studied regular lattices or complex networks differ from our new results.
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The Test of a New Critical Exponent Ϙ by Using Ising Model on the Creutz Cellular Automaton

88%
Merdan Z., Gokbel-Keklikoglu D.
Acta Physica Polonica A
|
2018
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vol. 133
|
issue 5
1200-1204
EN
Above the upper critical dimension d_{c} the Ising model is simulated on the Creutz cellular automaton. The values of a new critical exponent Ϙ are obtained by using the simulations for the order parameter and the magnetic susceptibility. At d=4,5,6,7,8, the values of the new critical exponent Ϙ are 0.9904(16), 1.2721(2), 1.4806(24), 1.7626(17), 1.9997(50) for the order parameter, respectively, while those 1.0415(13), 1.2987(27), 1.5133(1), 1.7741(1), 2.0133(28) are for the magnetic susceptibility in the same order. The computed values of the new critical exponent Ϙ are in agreement with theoretical values.
3
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Nematic ordering problem as the polymer problem of the excluded volume

75%
Yakunin A.
Open Physics
|
2003
|
vol. 1
|
issue 2
355-362
EN
Based on a solution of the polymer excluded volume problem, a technique is proposed to estimate some parameters at the isotropic-nematic liquid crystal phase transition (the product of the volume fraction of hard sticks and the ratio of the stick length, L, to its diameter, D; the maximum value of this ratio at which one cannot regard the stick as hard). The critical exponents are estimated. The transition of a swelling polymer coil to ideal is revealed as the polymerization degree of a macromolecule increases. The entanglement concentration obtained agrees with experimental data for polymers with flexible chains. The number of monomers between neighbor entanglements is assumed to be the ratio L/D. A comparison of the theory with other ones and recent experimental data is made.
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