Correlation functions of the One-Dimensional Random Field Ising Model at Zero Temperature

Abstract

We consider the one-dimensional random field Ising model, where the spin-spin coupling, $J$, is ferromagnetic and the external field is chosen to be $+h$ with probability $p$ and $-h$ with probability $1-p$. At zero temperature, we calculate an exact expression for the correlation length of the quenched average of the correlation function $⟨s_0{s}_n⟩-⟨s_0⟩⟨s_n⟩$ in the case that $2J/h$ is not an integer. The result is a discontinuous function of $2J/h$. When $p=\frac{1}{2}$, we also place a bound on the correlation length of the quenched average of the correlation function $⟨s_0{s}_n⟩$.

Comments: 12 pages (Plain TeX with one PostScript figure appended at end), MIT CTP #2202