Position space studies of the pure and dilute quantum Ising model. I. One-dimensional chain

A block-scaling method describing in a unified way quantum, thermal and random effects in the one-dimensional Ising model with a transverse field is presented. Reliable results have been obtained using a free-energy preserving mapping in a suitable cumulant-like approximation. At zero temperature a number of exact results characterising the quantum and percolative critical behaviour of the pure and dilute chain is recovered.

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