Exact Ground-State Energies of the Random-Field Ising Chain and Ladder

Abstract

We derive the exact ground-state energy of the one-dimensional Ising model in random fields taking values h, 0 and Àh with general probabilities. The random-field Ising model on a ladder is also analyzed by showing its equivalence to the random-field Ising chain with field values AEh and 0 for h < J. The zero-temperature transfer matrix is used to obtain the results.

Low-energy excitations in the three-dimensional random-field Ising model

“…Similar to the more prominent spin glasses (SGs) [2,3,4], there are still many open questions concerning the low-temperature properties of the RFIM. During the last few years, the RFIM and the related diluted antiferromagnet in a field have attracted growing attention [5,6,7,8,9,10,11,12,13,14,15,16], in particular within simulation studies at finite [17,18,19,20,21,22,23], and zero temperature [24,25,26,27,28,29,30,31,32,33,34,35,36].…”