Entropy of a random-bond Ising chain

We study the one-dimensional Ising model in a magnetic field with each nearest neighbor $J_i$ assigned at random. For $J_i=\pm J_0$ with equal probability, Nernst's law is violated, just as Kirkpatrick has found: however, when some uncertainty is introduced into the value of $J_0$ the entropy vanishes linearly with the temperature, much as in the mathematical two-level model for glasses of Anderson et al.