Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model
Abstract
We employ a mean-field approximation to study the Ising model with aperiodic modulation of its interactions in one spatial direction. Two different values for the exchange constant, JA and JB, are present, according to the Fibonacci sequence. We calculated the pseudo-critical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents β, δ, and γ and, from the usual scaling relations for anisotropic models at the upper critical dimension (assumed to be 4 for the model we treat), we calculate α, , //, η, and η//. Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents which depend on the ratio r JB/JA, as expected. But the scaling relation γ = β (δ -1) is obeyed for all values of r we studied. We characterize some thermodynamic functions as log-periodic functions of their arguments, as expected for aperiodic-modulated models, and obtain precise values for the exponents from this characterization.
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