An exactly solvable majority model

Domingo P. Prato, Carlos E. Budde and Mario A. Lamfri

Physica A: Statistical Mechanics and its Applications, 1994, vol. 206, issue 3, 581-586

Abstract: A bichromatic majority model is presented and studied analytically. The mean value of one color, say black, dominant cluster size is calculated as a function of the occupancy probability p for the black plaquettes, while 1−p=q is the occupancy probability for the white plaquettes. The model allows us to adopt different criteria for the definition of majority when a tie occurs, i.e. the numbers of black and white plaquettes are the same. This mean value shows a divergence with a critical exponent ν=1. The model is equivalent to a random walk with an absorbing barrier and a non-perfect trap. A Monte Carlo simulation of the process is performed giving agreement with the theoretical calculations. Some comments on the results obtained with the renormalization group are presented.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:206:y:1994:i:3:p:581-586

DOI: 10.1016/0378-4371(94)90325-5

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