Classical Annealing of Sherrington-Kirkpatrick Spin Glass Using Kubo-Suzuki Mean-field Ising Dynamics

Summary

The study proposes a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model using Kubo-Suzuki mean-field Ising dynamics. The results show that the ground state energy per spin scales as N^(-2/3) and the fluctuations in energy decrease as N^(-3/4), with an algorithmic cost of N^3.

Highlights

• The study uses Kubo-Suzuki mean-field Ising dynamics to simulate the SK spin glass model.
• The ground state energy per spin is found to scale as N^(-2/3).
• The fluctuations in energy decrease as N^(-3/4).
• The algorithmic cost is N^3.
• The study uses a modified Thouless-Anderson-Palmer reaction field.
• The results are verified through simulations of system sizes up to 8000.
• The ground state energy per spin is estimated to be -0.7633 ± 0.0003.

Key Insights

• The Kubo-Suzuki dynamics allow for a smoothening of the corrugated energy landscape, enabling the system to quickly orient in a low-energy configuration.
• The modified Thouless-Anderson-Palmer reaction field helps to avoid divergence in the T=0 limit.
• The study's results conform to established finite-size scaling relations for the SK model.
• The algorithmic cost of N^3 is significantly lower than previous estimates of N^4.
• The ground state energy per spin estimate of -0.7633 ± 0.0003 is consistent with earlier studies.
• The study's findings have implications for optimization problems and the development of more efficient algorithms.
• The use of Kubo-Suzuki dynamics and the modified Thouless-Anderson-Palmer reaction field provides a new approach to simulating spin glass models.

Mindmap

Citation

Das, S., Biswas, S., & Chakrabarti, B. K. (2024). Classical Annealing of Sherrington-Kirkpatrick Spin Glass Using Kubo-Suzuki Mean-field Ising Dynamics (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18358