Two-Stroke Pumping Technique for Many-Body Systems

Area of Science:

• Statistical Mechanics
• Computational Physics
• Sociophysics

Background:

• Estimating critical temperatures (Tc) in interacting many-body systems is crucial for understanding phase transitions.
• Existing methods like Monte Carlo sampling can be computationally intensive.

Purpose of the Study:

• Introduce a novel analytical framework, the two-stroke pumping technique (TSP), for estimating critical temperatures.
• Apply TSP to the Ising model across various dimensions and compare its efficiency and accuracy with existing methods.

Main Methods:

• Combined the Bethe cluster setting, Metropolis update, and Galam Majority Model.
• Developed a two-stroke pumping technique (TSP) for analytical estimation.
• Applied TSP to the Ising model in dimensions d=1, 2, 3, and 4.

Main Results:

• TSP yielded critical temperatures with an excess of +0.03 from exact estimates for d=2, 3, 4.
• Achieved the exact value of Tc=0 for d=1.
• Analytically demonstrated the impossibility of full symmetry breaking at T=0.
• Required significantly fewer computational resources than Monte Carlo sampling.

Conclusions:

• TSP provides computationally efficient and transparent calculations for critical temperatures.
• The framework is general and extendable to other discrete spin models.
• TSP is a scalable tool for studying cooperative behavior in interacting systems.