Low-temperature thermodynamics of random-field Ising chains: exact results

Abstract

The authors consider the random-field ferromagnetic Ising chain, for a class of continuous symmetric probability distributions of the random magnetic fields, of a diluted power-times-exponential type. This class of distribution is 'exactly solvable', in the sense that the disorder can be integrated explicitly, at any temperature. A detailed analysis of the low-temperature thermodynamics is presented. Exact expressions are obtained for the ground-state energy, the zero-temperature entropy, and the amplitude of the specific heat, which vanishes linearly at low temperature. The diluted symmetric binary distribution, where the magnetic fields can only assume the values +or-HB or zero, can be viewed as a limiting case of the class of exactly solvable distributions. The low-temperature physics of this discrete model is investigated in detail, including the exponential fall-off of the specific heat.