# Two-Stroke Pumping Technique for Many-Body Systems

## TL;DR

A new method called TSP is introduced to estimate critical temperatures in many-body systems, offering efficient and accurate results.

## Contribution

The novel two-stroke pumping technique combines sociophysics and statistical mechanics to estimate critical temperatures efficiently.

## Key findings

- TSP estimates critical temperatures with an excess of +0.03 in dimensions d=2,3,4.
- TSP confirms the exact critical temperature Tc=0 in d=1.
- TSP shows full symmetry breaking is practically impossible 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.