We study the use of effective transfer matrices for the numerical computation of masses (or correlation lengths) in lattice spin models. The effective transfer matrix has a strongly reduced number of components. Its definition is motivated by a renormalization group transformation of the full model onto a 1-dimensional spin model. The matrix elements of the effective transfer matrix can be determined by Monte Carlo simulation. We show that the mass gap can be recovered exactly from the spectrum of the effective transfer matrix. As a first step towards application we performed a Monte Carlo study for the 2-dimensional Ising model. For the simulations in the broken phase we employed a multimagnetical demon algorithm. The results for the tunnelling correlation length are particularly encouraging.

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