Adaptive dynamics of Ising spins in one dimension leveraging Reinforcement Learning

TL;DR

This paper investigates a one-dimensional active Ising spin system using reinforcement learning, revealing four phases including a novel oscillatory phase with chaotic dynamics, and showing that RL can replicate known behaviors without explicit interactions.

Contribution

It introduces a reinforcement learning framework to study active Ising spins, discovering new phases and dynamics without explicit spin interactions.

Findings

Identified four phases: disorder, flocking, flipping, and oscillatory.

Reversal time exponentially decays with noise parameter b5.

Discovered a chaotic oscillatory phase with positive Lyapunov exponent.

Abstract

A one-dimensional flocking model using active Ising spins is studied, where the system evolves through the reinforcement learning approach \textit{via} defining state, action, and cost function for each spin. The orientation of spin with respect to its neighbouring spins defines its state. The state of spin is updated by altering its spin orientation in accordance with the $\varepsilon$-greedy algorithm (action) and selecting a finite step from a uniform distribution to update position. The $\varepsilon$ parameter is analogous to the thermal noise in the system. The cost function addresses cohesion among the spins. By exploring the system in the plane of the self-propulsion speed and $\varepsilon$ parameter, four distinct phases are found: disorder, flocking, flipping, and oscillatory. In the flipping phase, a condensed flock reverses its direction of motion stochastically. The mean reversal time $\langle T \rangle $ exponentially decays with $\varepsilon$. A new phase, an oscillatory phase, is also found, which is a chaotic phase with a positive Lyapunov exponent. The findings obtained from the reinforcement learning approach for the active Ising model system exhibit similarities with the outcomes of other conventional techniques, even without defining any explicit interaction among the spins.