  We present an alternative procedure for solving the eigenvalue problem of
replicated transfer matrices describing disordered spin systems with (random)
1D nearest neighbor bonds and/or random fields, possibly in combination with
(random) long range bonds. Our method is based on transforming the original
eigenvalue problem for a $2^n\times 2^n$ matrix (where $n\to 0$) into an
eigenvalue problem for integral operators. We first develop our formalism for
the Ising chain with random bonds and fields, where we recover known results.
We then apply our methods to models of spins which interact simultaneously via
a one-dimensional ring and via more complex long-range connectivity structures,
e.g. $1+\infty$ dimensional neural networks and `small world' magnets.
Numerical simulations confirm our predictions satisfactorily.
