Universal Critical Jump for Inverse-Square Ising Ferromagnets

Abstract

For every translation-invariant ferromagnetic Ising chain with $n^2J_n\to B>0$, we prove $2β_cBm_c^2=1$, without restrictions on the finite core or the tail convergence rate. The proof bounds the energy of macroscopic interfaces and rules them out if the critical product exceeds one. Despite the nonzero jump, connected susceptibility is infinite both at criticality and in a neighboring ordered interval. At the critical coupling, the excess magnetization decays more slowly than any positive power of the field as the field tends to zero. We also prove the jump relation in continuous time, for a positive-Stieltjes class of Ohmic spin-boson models.