A Simple Re-Derivation of Onsager's Solution of the 2D Ising Model using Experimental Mathematics

TL;DR

This paper demonstrates how experimental mathematics and symbolic computation can re-derive Onsager's 2D Ising model solution more straightforwardly, emphasizing practicality over strict rigor.

Contribution

It presents a new, simpler derivation of Onsager's solution using experimental mathematics, bypassing complex traditional proofs.

Findings

Re-derivation confirms Onsager's solution without rigorous proof

Highlights the effectiveness of experimental mathematics in physics

Simplifies understanding of the 2D Ising model solution

Abstract

In this case study, we illustrate the great potential of experimental mathematics and symbolic computation, by rederiving, ab initio, Onsager's celebrated solution of the twodimensional Ising model in zero magnetic field. Onsager's derivation is extremely complicated and ad hoc, as are all the subsequent proofs. Unlike Onsager's, our derivation is not rigorous, yet it is absolutely certain (even if Onsager did not do it before), and should have been acceptable to physicists who do not share mathematicians' fanatical (and often misplaced) insistence on rigor.