Universal features of exit probability in opinion dynamics models with domain size dependent dynamics

作者：Roy Parna^*; Biswas Soham; Sen Parongama

来源：Journal of Physics A-Mathematical and Theoretical, 2014, 47(49): 495001.

DOI：10.1088/1751-8113/47/49/495001

• scaling behaviour
• universality class
• dynamical exponents

We study the exit probability for several binary opinion dynamics models in one dimension in which the opinion state (represented by +/- 1) of an agent is determined by dynamical rules dependent on the size of its neighbouring domains. In all these models, we find the exit probability behaves like a step function in the thermodynamic limit. In a finite system of size L, the exit probability E(x) as a function of the initial fraction x of one type of opinion is given by E(x) = f[(x - x(c)) L-1/nu] with a universal value of nu= 2.5 +/- 0.03. The form of the scaling function is also universal: f (y) = [tanh (lambda y+ c)+ 1]/2, where lambda is found to be dependent on the particular dynamics. The variation of lambda against the parameters of the models is studied. c is non-zero only when the dynamical rule distinguishes between +/- 1 states; comparison with theoretical estimates in this case shows very good agreement.

• 出版日期2014-12-12