Decimation method for two-dimensional Ising exponents

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Abstract
We have applied a decimation (dedecoration) method to a quantum system in order to obtain a critical exponent of the two-dimensional Ising model. Because the renormalization-group transformation is not exact, we have used a perturbation similar to the one used by Niemeijer and Van Leeuwen. The calculations were done to third order. Contrary to the 3-spin-cell method, the second order generates only next-nearest interaction, while the third order generates the next-next-nearest neighbor, etc. The numerical results are compared and analyzed. There are oscillations in our calculation, and the perturbation seems to be at least asymptotic.