A Cluster Expansion and the Decay of Correlations of the 1D Long-Range Ising Model at Low Temperatures
Abstract
In this work, a convergent low-temperature cluster expansion of the one-dimensional long-range ferromagnetic Ising model with polynomial decay $α\in (1,2]$ is developed; that is, $J(r)=r^{-α}$. As an application, the $n$-point correlations are studied and the two-point correlation is shown to be algebraic with rate of decay exactly $α$.
Fields of Study & Subjects
Theoretical and Computational Physics
Stochastic processes and statistical mechanics
advanced mathematical theories
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 February 2026
- Language
- EN
- Document type
- Preprint