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Ordering through learning in two-dimensional Ising spins.

Pranay Bimal Sampat1,2, Ananya Verma1, Riya Gupta1

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Physical Review. E
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This summary is machine-generated.

Reinforcement learning models two-dimensional Ising spins, mimicking phase transitions. Tuning the epsilon parameter reveals critical exponents analogous to the Ising model, especially at lower learning rates.

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Area of Science:

  • Statistical Mechanics
  • Machine Learning
  • Computational Physics

Background:

  • The two-dimensional Ising model is a fundamental model in statistical mechanics exhibiting phase transitions.
  • Reinforcement learning offers a novel framework for studying complex systems dynamics.
  • Understanding phase transitions is crucial for diverse fields, from condensed matter physics to critical phenomena.

Purpose of the Study:

  • To investigate the application of reinforcement learning to model phase transitions in a two-dimensional Ising spin system.
  • To explore the relationship between the reinforcement learning parameter epsilon and temperature in the Ising model.
  • To calculate critical exponents and verify hyperscaling relations using a machine learning approach.

Main Methods:

  • Simulating two-dimensional Ising spins using a reinforcement learning agent.
  • Defining spin states based on neighbor majority/minority and updating via an epsilon-greedy algorithm.
  • Tuning the epsilon parameter to induce and analyze phase transitions, calculating critical exponents (beta, gamma, nu).

Main Results:

  • A phase transition from an ordered to a disordered state was observed as epsilon increased.
  • Critical exponents beta, gamma, and nu were calculated, consistent with the Ising model.
  • A hyperscaling relation (d*nu = 2*beta + gamma) was confirmed.
  • Exponents approached exact Ising model values at lower learning rates.

Conclusions:

  • Reinforcement learning can effectively model and reproduce phase transitions observed in the two-dimensional Ising model.
  • The epsilon parameter in the reinforcement learning algorithm serves as an effective analog to temperature.
  • Lower learning rates in the reinforcement learning framework yield more accurate critical exponent values, aligning with theoretical predictions.