Solving spin glasses with optimized trees of clustered spins

Area of Science:

• Statistical physics
• Computational methods

Background:

• Spin glasses and Ising models are complex systems with applications in various fields.
• Efficiently optimizing and sampling these systems is computationally challenging.

Purpose of the Study:

• To develop a novel algorithm for the optimization and thermal equilibration of spin glasses and Ising models.
• To improve sampling efficiency for complex systems defined on arbitrary graphs.

Main Methods:

• The algorithm employs a two-step iterative process: optimized construction of random tree clusters and thermal sampling of these trees.
• Trees are generated to balance size and sampling complexity, enabling efficient Boltzmann sample generation.

Main Results:

• The algorithm demonstrates superior performance compared to existing methods on benchmark problems.
• It provides an efficient approach for thermal equilibration and optimization of spin glass systems.

Conclusions:

• The presented algorithm offers a significant advancement in the computational study of spin glasses and Ising models.
• This method enhances the ability to explore complex energy landscapes in statistical physics.