We introduce a stochastic model of binary opinion dynamics in which the opinions are determined by the size of the neighboring domains. The exit probability here shows a step function behavior, indicating the existence of a separatrix distinguishing two different regions of basin of attraction. This behavior, in one dimension, is in contrast to other well known opinion dynamics models where no such behavior has been observed so far. The coarsening study of the model also yields novel exponent values. A lower value of persistence exponent is obtained in the present model, which involves stochastic dynamics, when compared to that in a similar type of model with deterministic dynamics. This apparently counterintuitive result is justified using further analysis. Based on these results, it is concluded that the proposed model belongs to a unique dynamical class.

PARONGAMA SEN

Physics

SOHAM BISWAS

SUMAN SINHA

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Physical Review E

A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening dynamics of the equivalent Ising model shows power law behavior and has been found to belong to a new universality class with the dynamic exponent z = 1.0 ± 0.01 and persistence exponent θ ≃ 0.235 in one dimension. The critical behavior has been found to be robust for a large variety of annealed disorder that has been studied. Further, by mapping Model I to a system of random walkers in one dimension with a tendency to walk towards their nearest neighbour with probability ε, we find that for any ε > 0.5, the Model I dynamical behaviour is prevalent at long times.

Journal of Physics: Conference Series

Opinion dynamics model with domain size dependent dynamics: Novel features and new universality class

The dynamical evolution of a recently introduced one-dimensional model (henceforth, referred to as model I), has been made stochastic by introducing a parameter β such that β=0 corresponds to the Ising model and β→∞ to the original model I. The equilibrium behavior for any value of β is identical: a homogeneous state. We argue, from the behavior of the dynamical exponent z, that for any β 0, the system belongs to the dynamical class of model I indicating a dynamic phase transition at β=0. On the other hand, the persistence probabilities in a system of L spins saturate at a value Psat (β,L) = ( β/L ) α f (β), where α remains constant for all β ≠ 0 supporting the existence of the dynamic phase transition at β =0. The scaling function f (β) shows a crossover behavior with f (β) = constant for β □ 1 and f (β) □ β - α for β □1 . © 2010 The American Physical Society.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Noise-driven dynamic phase transition in a one-dimensional Ising-like model

We propose a model of binary opinion in which the opinion of the individuals changes according to the state of their neighboring domains. If the neighboring domains have opposite opinions then the opinion of the domain with the larger size is followed. Starting from a random configuration, the system evolves to a homogeneous state. The dynamical evolution shows a scaling behavior with the persistence exponent θ0.235 and dynamic exponent z1.02±0.02. Introducing disorder through a parameter called rigidity coefficient ρ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at ρ= 0+ is obtained. Close to ρ=0, the equilibrium values of the dynamic variables show power-law scaling behavior with ρ. We also discuss the effect of having both quenched and annealed disorder in the system. © 2009 The American Physical Society.

Model of binary opinion dynamics: Coarsening and effect of disorder

We investigate the dynamics of a two-dimensional axial next-nearest-neighbor Ising model following a quench to zero temperature. The Hamiltonian is given by H=-J(0)Sigma(L)(i,j=1)S(i,j)S(i+1,j)-J(1)Sigma(i,j=1)(S(i,j)S(i,j+1)-kappa S(i,j)S(i,j+2)). For kappa < 1, the system does not reach the equilibrium ground state but slowly evolves to a metastable state. For kappa>1, the system shows a behavior similar to that of the two-dimensional ferromagnetic Ising model in the sense that it freezes to a striped state with a finite probability. The persistence probability shows algebraic decay here with an exponent theta=0.235 +/- 0.001 while the dynamical exponent of growth z=2.08 +/- 0.01. For kappa=1, the system belongs to a completely different dynamical class; it always evolves to the true ground state with the persistence and dynamical exponent having unique values. Much of the dynamical phenomena can be understood by studying the dynamics and distribution of the number of domain walls. We also compare the dynamical behavior to that of a Ising model in which both the nearest and next-nearest-neighbor interactions are ferromagnetic.

Journal	Physical Review E
Publisher	AMER PHYSICAL SOC
ISSN	2470-0045
Open Access	Yes