The critical properties of the Ising model on the Penrose lattice of a size up to 439,204 sites are studied by means of the Monte Carlo simulation. We make an analysis of a phenomenological Monte Carlo renormalization group based on finite-size scaling. The critical temperature T c and the magnetic critical exponent y H are obtained to be (2.392±0.004) J and 1.89±0.02. The value of y H coincides with the value of a two-dimensional crystal, y H =1.875, within numerical accuracy.
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Okabe et al. (1988) studied this question.
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