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We present an alternative procedure for solving the eigenvalue problem ofreplicated 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 originaleigenvalue problem for a $2^n\times 2^n$ matrix (where $n\to 0$) into aneigenvalue problem for integral operators. We first develop our formalism forthe Ising chain with random bonds and fields, where we recover known results.We then apply our methods to models of spins which interact simultaneously viaa 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.Comment: 24 pages, LaTex, IOP macro

Diagonalization of replicated transfer matrices for disordered Ising spin systems