arXiv subjects
Publications and source records attributed to Henrique Corsini.
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 $α$.
Following seminal work by J. Fröhlich and T. Spencer on the critical exponent $α=2$, we give a proof via contours of phase transition in the one-dimensional long-range ferromagnetic Ising model in the entire region of decay, where phase transition is known to occur, i.e., polynomial decay $α\in (1,2]$. No assumptions that the nearest-neighbor interaction $J(1)$ is large are made. The robustness of the method also yields a proof of phase transition in the presence of a nonsummable external field that decays sufficiently fast.