Non-universal behavior for aperiodic interactions within a mean-field approximation

Details Non-universal behavior for aperiodic interactions within a mean-field approximation Non-universal behavior for aperiodic interactions within a mean-field approximation

2008-03-14

arxiv.org/abs/0803.2155v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, 7 figures, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.77.041113

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following two deterministic aperiodic sequences: Fibonacci or period-doubling ones. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponent $\beta$, $\gamma$ and $\delta$. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

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