Random-bond Ising chain in a magnetic field at low temperatures

Abstract

The low-temperature behavior ($T\ensuremath{\ll}h, J$) of a random-bond Ising chain in a magnetic field is considered [$H=\ensuremath{-}(\frac{1}{2})J\ensuremath{\Sigma}{T}_{i}{\ensuremath{\sigma}}_{i}{\ensuremath{\sigma}}_{i+1}\ensuremath{-}h\ensuremath{\Sigma}{\ensuremath{\sigma}}_{i}, {\ensuremath{\sigma}}_{i}=\ifmmode\pm\else\textpm\fi{}1$, ${{T}_{i}}$ is a fixed random sequence of numbers +1 and -1 with concentrations ${c}_{1}$ and ${c}_{2}=1\ensuremath{-}{c}_{1}$, respectively]. The ground-state energy ${E}_{0}$, magnetization ${\ensuremath{\mu}}_{0}$ and zero-point entropy ${S}_{0}$ are calculated exactly. It is shown that ${\ensuremath{\mu}}_{0}$ and ${S}_{0}$ are discontinuous functions of magnetic field having jumps at $h=\frac{J}{n}$, $n=1, 2, \dots{}$.