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February 12, 2026Open Access

Two-Stroke Pumping Technique for Many-Body Systems

Key Points

The aim is to present a new method for estimating critical temperatures in interacting many-body systems using the Ising model.
Introduces a two-stroke pumping technique (TSP) integrating multiple analytical models.
Applies TSP to the Ising model across dimensions d=2,3,4.
Demonstrates computational efficiency compared to Monte Carlo sampling.
TSP yields critical temperatures with an accuracy of +0.03 from exact values in higher dimensions.
Exact critical value obtained at d=1 is Tc=0.
Indicates difficulty in achieving full symmetry breaking at T=0.

Abstract

I introduce a new analytical framework for estimating critical temperatures in interacting many-body systems, focusing on the Ising model. Combining the Bethe cluster setting, the Metropolis update, and the Galam Majority Model developed in sociophysics, I build a two-stroke pumping technique (TSP). Applied to the Ising model in dimensions d=2,3,4, TSP yields values of Tc which are all at an excess of +0.03 from exact estimates. At d=1, the exact value Tc=0 is obtained. In addition, TSP analytically indicates the practical impossibility of reaching full symmetry breaking at T=0. The results are thus found in good agreement with numerical findings while requiring significantly fewer computational resources than Monte Carlo sampling. Calculations are computationally efficient and transparent. The framework is general and can be extended to a broad class of discrete spin models. This positions TSP as an intermediate yet scalable tool for studying cooperative behavior in many-body interacting systems.

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