AUTHOR=Lima Francisco W. S. 

TITLE=Kinetic Continuous Opinion Dynamics Model on Two Types of Archimedean Lattices

JOURNAL=Frontiers in Physics

VOLUME=5

YEAR=2017

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2017.00047

DOI=10.3389/fphy.2017.00047

ISSN=2296-424X

ABSTRACT=<p>Here, the critical properties of kinetic continuous opinion dynamics model are studied on (4, 6, 12) and (4, 8<sup>2</sup>) Archimedean lattices. We obtain <italic>p</italic><sub><italic>c</italic></sub> and the critical exponents from Monte Carlo simulations and finite size scaling. We found out the values of the critical points and Binder cumulant that are <italic>p</italic><sub><italic>c</italic></sub> = 0.086(3) and <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>59</mml:mn><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> for (4, 6, 12); and <italic>p</italic><sub><italic>c</italic></sub> = 0.109(3) and <inline-formula><mml:math id="M2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:mn>606</mml:mn><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> for (4, 8<sup>2</sup>) lattices and also the exponent ratios β/ν, γ/ν, and 1/ν are, respectively: 0.23(7), 1.43(5), and 0.60(3) for (4, 6, 12); and 0.149(4), 1.56(4), and 0.94(4) for (4, 8<sup>2</sup>) lattices. Our new results disprove of the Grinstein criterion.</p>