Emergence of log-periodic oscillations in periodic and aperiodic Ising models

Andrade, Roberto F. S.

doi:10.1590/s0103-97332000000400006

Cited by 2 publications

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“…where Θ(L) stands for the slope of the straight line at a given L and Θ stands for γ/ν or β/ν, depending on whether we use the data for χ(T c ) or m(T c ), respectively. This shows the expected behavior for systems with aperiodic modulations [26,27].…”

Section: Resultssupporting

confidence: 64%

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Influence of aperiodic modulations on first-order transitions: Numerical study of the two-dimensional Potts model

Girardi

Branco

2011

Phys. Rev. E

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We study the Potts model on a rectangular lattice with aperiodic modulations in its interactions along one direction. Numerical results are obtained using the Wolff algorithm and for many lattice sizes, allowing for a finite-size scaling analyses to be carried out. Three different self-dual aperiodic sequences are employed, which leads to more precise results, since the exact critical temperature is known. We analyze two models, with 6 and 15 number of states: both present first-order transitions on their uniform versions. We show that the Harris-Luck criterion, originally introduced in the study of continuous transitions, is obeyed also for first-order ones. Also, we show that the new universality class that emerges for relevant aperiodic modulations depends on the number of states of the Potts model, as obtained elsewhere for random disorder, and on the aperiodic sequence. We determine the occurrence of log-periodic behavior, as expected for models with aperiodic modulated interactions.

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Section: Resultssupporting

confidence: 64%

“…6(b) and 6(c) for small values of 1/pL min shows that the convergence to the thermodynamic limit is not the usual one: oscillations are present for both β/ν and γ /ν, and they do not die out for the largest lattices. This behavior maybe a sign of log-periodic oscillations, expected to be present in models with aperiodic modulations [26,27].…”

Section: Resultsmentioning

confidence: 77%

Influence of aperiodic modulations on first-order transitions: Numerical study of the two-dimensional Potts model

Girardi

Branco

2011

Phys. Rev. E

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Critical behavior of a contact process with aperiodic transition rates

2008

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We performed Monte Carlo simulations to investigate the steadystate critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

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Emergence of log-periodic oscillations in periodic and aperiodic Ising models

Cited by 2 publications

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Influence of aperiodic modulations on first-order transitions: Numerical study of the two-dimensional Potts model

Influence of aperiodic modulations on first-order transitions: Numerical study of the two-dimensional Potts model

Critical behavior of a contact process with aperiodic transition rates

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