Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model.
Phys Rev E Stat Nonlin Soft Matter Phys
; 85(1 Pt 1): 011113, 2012 Jan.
Article
em En
| MEDLINE
| ID: mdl-22400518
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, J(A) and J(B), are present, according to the Fibonacci sequence. We calculate the pseudocritical temperatures for finite systems and extrapolate them to the thermodynamic limit. We explicitly obtain the exponents ß, 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, ν, ν(â¥), η, and η(â¥). Within the framework of a renormalization-group approach, the Fibonacci sequence is a marginal one and we obtain exponents that depend on the ratio r≡J(B)/J(A), as expected; however, the scaling relation γ=ß(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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01-internacional
Base de dados:
MEDLINE
Assunto principal:
Algoritmos
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Modelos Moleculares
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Modelos Químicos
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Assunto da revista:
BIOFISICA
/
FISIOLOGIA
Ano de publicação:
2012
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos