  The interpolation method is a powerful tool for rigorous analysis of
mean-field spin glass models, both with and without dilution. In this study, we
show that the interpolation method can be applied to Ising spin glass models in
one dimension, such as a one-dimensional chain and a two-leg ladder. In one
dimension, the replica symmetric (RS) cavity method is naturally expected to be
rigorous for Ising spin glass models. Using the interpolation method, we
rigorously prove that the RS cavity method provides lower bounds on the
quenched free energies of Ising spin glass models in one dimension at any
finite temperature in the thermodynamic limit.
