Exit Probability in Generalised Kinetic Ising Model

TL;DR

This paper analyzes the exit probability in generalized one-dimensional kinetic Ising models with information inflow, highlighting the accuracy of analytical methods for nearest-neighbor interactions and deviations for longer-range interactions.

Contribution

It derives analytical expressions for exit probability in generalized Ising Glauber models and compares their accuracy across different interaction ranges.

Findings

Analytical results match simulations for nearest-neighbor interactions.

Deviations increase as interaction range extends beyond nearest neighbors.

Discussion of reasons behind deviations and open questions.

Abstract

In this paper we study generalised Ising Glauber models with inflow of informa- tion in one dimension and derive expressions for the exit probability using well established analytical methods. The analytical expressions agree very well with the results obtained from numerical simulation only when the interaction is restricted to the nearest neighbor. But as the range of interaction is increased the analytical results deviate from simulation results systematically. The reasons for the deviation as well as some related open questions are discussed.