Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry and fluctuation

Abstract

Probing deeper into the existing issues regarding the exit probability (EP) in one dimensional dynamical models, we consider several models where the states are represented by Ising spins and the information flows inwards. At zero temperature, these systems evolve to either of two absorbing states. The exit probability $E(x)$, which is the probability that the system ends up with all spins up starting with $x$ fraction of up spins is found to have the general form $E(x)=x^{\alpha }/\left[x^{\alpha }+(1-x{)}^{\alpha }\right]$. The exit probability exponent $\alpha$ strongly depends on $r$, the range of interaction, the symmetry of the model and the induced fluctuation. Even in a nearest neighbour model, nonlinear form of EP can be obtained by controlling the fluctuations and for the same range, different models give different results for $\alpha$. Non-universal behaviour of the exit probability is thus clearly established and the results are compared to existing studies in models with outflow dynamics to distinguish the two dynamical scenarios.

5 pages, 6 figures

References in corpus (6)

• Statistical physics of social dynamics
• Dynamics of Non-Conservative Voters
• Some new results on one-dimensional outflow dynamics
• Metastability in zero-temperature dynamics: Statistics of attractors
• Irrelevance of information outflow in opinion dynamics models
• Inflow versus outflow zero-temperature dynamics in one dimension

Cited by in corpus (12)

• Phase transitions in the q-voter model with noise on a duplex clique
• Inflexibility and independence: Phase transitions in the majority-rule model
• Long route to consensus: Two stage coarsening in a binary choice voting model
• Kinetic Ising models with various single-spin flip dynamics on quenched and annealed random regular graphs
• Mapping the $q$-voter model: From a single chain to complex networks
• Interplay of interfacial noise and curvature driven dynamics in two dimensions
• Zero temperature coarsening in Ising model with asymmetric second neighbour interaction in two dimensions
• Exit Probability in Generalised Kinetic Ising Model
• Phase diagram in a one-dimensional civil disorder model
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Universal features of exit probability in opinion dynamics models with domain size dependent dynamics
• Non-equilibrium dynamics in Ising like models with biased initial condition