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We employ a mean-field approximation to study the Ising model with aperiodicmodulation of its interactions in one spatial direction. Two different valuesfor the exchange constant, $J_A$ and $J_B$, are present, according to theFibonacci sequence. We calculated the pseudo-critical temperatures for finitesystems and extrapolate them to the thermodynamic limit. We explicitly obtainthe exponents $\beta$, $\delta$, and $\gamma$ and, from the usual scalingrelations for anisotropic models at the upper critical dimension (assumed to be4 for the model we treat), we calculate $\alpha$, $\nu$, $\nu_{//}$, $\eta$,and $\eta_{//}$. Within the framework of a renormalization-group approach, theFibonacci sequence is a marginal one and we obtain exponents which depend onthe ratio $r \equiv J_B/J_A$, as expected. But the scaling relation $\gamma =\beta (\delta -1)$ is obeyed for all values of $r$ we studied. We characterizesome thermodynamic functions as log-periodic functions of their arguments, asexpected for aperiodic-modulated models, and obtain precise values for theexponents from this characterization.

Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model