2025/08/30 by Mário J. de Oliveira, de Oliveira, Mário J. · 2 voices
Materials Science · Physics and Astronomy · #Chain (unit) #Connection (principal bundle) #Ferromagnetism #Ising model #Magnetism in coordination complexes #Opinion Dynamics and Social Influence #Square-lattice Ising model #State (computer science) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2509.00632
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In 1925, Ernest Ising published a paper analyzing a model proposed in 1920 by Wilhelm Lenz for ferromagnetism. The model is composed of constituent units that take only two states and interact only when they are neighbors. Ising showed that in a linear chain the model does not present an ordered ferromagnetic state, a frustrating but correct result. However, Rudolf Peierls demonstrated in 1936 that the model does in fact present an ordered state in two dimensions, and therefore in three dimensions. This result reveals that short-range interaction and only two states for each constituent unit are sufficient for ordering to occur over long distances. These two elements are the key to understanding the success of the model and its variants even a hundred years after its appearance. Here we analyze the emergence of the model in the period up to 1936.