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 - h 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 ± h and 0 for h < J . The zero-temperature transfer matrix is used to obtain the results.