Impurities in Ising-model lattices and probe independence of hyperfine critical exponents

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Abstract
The spin -1/2 Ising Hamiltonian with a single non-magnetic impurity is analysed. An exact expression in terms of perfect lattice correlation functions is found for the average value of the spin on a site neighbouring the impurity. The latter quantity is a measure of the importance of probe disturbance effects in hyperfine field measurements of critical exponents. It is shown for the case of a simple cubic lattice that the hyperfine probe does not disturb the measurement of the critical exponent beta if the temperature is in the presently experimentally accessible range close to the critical temperature. It is also found that mean-field theories overestimate the importance of probe disturbance effects.