Two stroke Pumping Technique for Many-Body Systems

TL;DR

This paper introduces the Two Stroke Pumping (TSP) technique, an analytical method combining sociophysics models to estimate critical temperatures in many-body systems like the Ising model, achieving accurate results with less computational effort.

Contribution

The paper presents a novel analytical framework, TSP, that accurately estimates critical temperatures in many-body systems using a combination of sociophysics models, offering a scalable alternative to numerical methods.

Findings

TSP estimates T_c within +0.03 of exact values for 2D, 3D, 4D Ising models.

TSP correctly predicts T_c=0 for 1D Ising model.

TSP demonstrates the practical impossibility of 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 T_c which are all at an excess of +0.03 from exact estimates. At d=1 the exact value T_c=0 is obtained. In addition, TSP indicates analytically the practical impossibility to reach 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.