SWAP algorithm for lattice spin models

Area of Science:

• Computational Physics
• Statistical Mechanics
• Materials Science

Background:

• Lattice Ising spin models are crucial for understanding magnetism and complex systems.
• Traditional Monte Carlo methods can be slow, especially at low temperatures.
• Efficient exploration of energy landscapes is vital for finding ground states.

Purpose of the Study:

• To adapt the SWAP molecular dynamics algorithm for lattice Ising spin models.
• To investigate the efficiency of the adapted algorithm in accelerating simulations.
• To explore the relationship between dynamics and free-energy landscapes in spin systems.

Main Methods:

• Adapted the SWAP algorithm by dressing spins with random lengths.
• Alternated long-range spin exchanges with single spin flip Monte Carlo updates.
• Employed a stochastic acceptance rule that respects detailed balance.

Main Results:

• The adapted SWAP algorithm significantly accelerates relaxation in the bidimensional Edwards-Anderson model at low temperatures.
• The method demonstrates high efficiency in finding ground states with low computational cost.
• Provides insights into the acceleration mechanism of SWAP in particle systems.

Conclusions:

• The SWAP algorithm is an effective tool for simulating lattice Ising spin models.
• This approach enhances computational efficiency for exploring complex spin dynamics.
• The study illuminates the connection between simulation dynamics and system free-energy landscapes.