Nonuniversal behavior for aperiodic interactions within a mean-field approximation

Faria, Maicon S.; Branco, N. S.; Tragtenberg, M. H. R.

doi:10.1103/physreve.77.041113

Cited by 6 publications

(12 citation statements)

References 21 publications

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“…For models that have a continuous transition in its uniform version, the influence of aperiodic modulations on their critical behavior is determined by the Harris-Luck criterion [4] (which seems to hold true for models with first-order transition as well [5]). According to this criterion, the Fibonacci sequence is a marginal one; several results show that a marginal perturbation leads to a dependence of the critical exponents on the ratio between the two different interactions [6][7][8]. Using the simplest version of a meanfield approximation, we confirm these results and expand them to include other critical exponents, in order to test scaling relations, and to characterize log-periodic oscillations.…”

Section: Introductionsupporting

confidence: 59%

“…As discussed elsewhere [6,8,14] , this quantity may be experimentally accessible. We now have to extrapolate the values obtained for L → ∞.…”

Section: B Magnetizationmentioning

confidence: 99%

“…The mean-field value for the critical exponent of the uniform case is 1; our evaluation is 0.1 % off. r γ γ cal = β(δ − 1) ∆γ(%) 0.5 0.9557 (8) 0.9511(5) 0.5 0.7 0.9812 (8) 0.97522(5) 0.6 1.0 1.0010(3)…”

Section: Critical Exponent γmentioning

confidence: 99%

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

Ns²

2012

Phys. Rev. E

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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 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, ν, ν(∥), η, and η(∥). 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=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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Section: Introductionsupporting

confidence: 59%

“…As discussed elsewhere [6,8,14] , this quantity may be experimentally accessible. We now have to extrapolate the values obtained for L → ∞.…”

Section: B Magnetizationmentioning

confidence: 99%

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

Ns²

2012

Phys. Rev. E

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“…To complete this inequality parameters set of the Brazilian population we calculate the Gini coefficient associating the Brown's formula and the method of convergent extrapolation oscillation [4]. This methodology allowed us to verify that the measure of the degree of uncertainty associated with this estimate is virtually nil due to extreme convergence.…”

Section: Pnad Of 2014mentioning

confidence: 99%

Kinetic theory and Brazilian income distribution

Siciliani

Tragtenberg

2019

Physica A: Statistical Mechanics and its Applications

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We investigate the Brazilian personal income distribution using data from National Household Sample Survey (PNAD), an annual research available by the Brazilian Institute of Geography and Statistics (IBGE). It provides general characteristics of the country's population. Using PNAD data background we also confirm the effectiveness of a semi-empirical model that reconciles Pareto power-law for high-income people and Boltzmann-Gibbs distribution for the rest of population. We use three measures of income inequality: the Pareto index, the average income and the crossover income. In order to cope with many dimensions of the income inequality, we calculate these three indices and also the Gini coefficient for the general population as well as for two kinds of population dichotomies: black/ indigenous /mixed race versus white / yellow; and men versus women. We also followed the time series of these indices for the period 2001-2014. The results suggest a decreasing of Brazilian income inequality over the selected period. Another important result is that historically-disadvantaged subgroups (Women and black / indigenous / mixed race),that are the majority of the population, have a more equalitarian income distribution. These groups have also a smaller monthly income than the others and this social structure remained virtually unchanged in the period of time.

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“…Devemos também incluir uma análise de tamanho finito (finite size scaling) consistente com o comportamento de sistemas aperiódicos [13].…”

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Comportamento crítico do processo de contato aperiódico: simulações e grupo de renormalização

Faria¹

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We use an operator formalism and the renormalization-group technique of Dasgupta, Ma and Hu to analyze the effects of a nonhomogeneous distribution of parameters on the critical behavior of simple stochastic model system. The contact process in one dimension is perhaps the simplest model to display a phase transition to an absorbing stationary state. We use the Fibonacci, period-doubling and period-tripling sequences for introducing aperiodic inhomogeneities in the one dimensional contact process and in a quantum Ising chain. Using strong-disorder renormalization-group procedures, we establish some relations between properties of renormalized operator and of thermodynamic or mean quantities. We were able to test a well-known criterion of relevance of geometric fluctuations, to obtain a number of critical exponents, and to point out features of slow-dynamics and log-periodic oscillations. The period-tripling sequence leads to the critical exponents β = ln (7/9)/ ln (4/9), δ = ln (9/7)/ ln 4, ν ⊥ = ln 3/ ln (3/2) and ν = ln 2/ ln (3/2). We then used Monte Carlo techniques to check renormalization-group results. The numerical simulations indicate the validity of the Harris-Luck criterion of relevance of the geometric fluctuations, and generally support the universal character of the critical behavior of these aperiodic systems.

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Nonuniversal behavior for aperiodic interactions within a mean-field approximation

Cited by 6 publications

References 21 publications

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

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

Kinetic theory and Brazilian income distribution

Comportamento crítico do processo de contato aperiódico: simulações e grupo de renormalização

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