Ordering through learning in two-dimensional Ising spins

We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates its state using an {\epsilon}-greedy algorithm. The parameter...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Sampat, Pranay Bimal, Verma, Ananya, Gupta, Riya, Mishra, Shradha
Format: Article
Language:English
Subjects:
Exponents
Greedy algorithms
Ising model
Learning
Phase transitions
Online Access:Get full text
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Summary:We study two-dimensional Ising spins, evolving through reinforcement learning using their state, action, and reward. The state of a spin is defined as whether it is in the majority or minority with its nearest neighbours. The spin updates its state using an {\epsilon}-greedy algorithm. The parameter {\epsilon} plays the role equivalent to the temperature in the Ising model. We find a phase transition from long-ranged ordered to a disordered state as we tune {\epsilon} from small to large values. In analogy with the phase transition in the Ising model, we calculate the critical {\epsilon} and the three critical exponents {\beta}, {\gamma}, {\nu} of magnetization, susceptibility, and correlation length, respectively. A hyper-scaling relation d{\nu} = 2{\beta} + {\gamma} is obtained between the three exponents. The system is studied for different learning rates. The exponents approach the exact values for two-dimensional Ising model for lower learning rates.
ISSN:2331-8422