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

TL;DR

This paper derives exact ground-state energies for the 1D random-field Ising model and its ladder variant, providing precise solutions for these disordered quantum systems using transfer matrix methods.

Contribution

It presents the first exact solutions for the ground-state energies of the random-field Ising chain and ladder, extending understanding of disordered magnetic systems.

Findings

Exact ground-state energies derived for the 1D random-field Ising model.

Equivalence established between the ladder and chain models under certain conditions.

Utilization of transfer matrix method for precise energy calculations.

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