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

Abstract

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.

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

References in corpus (3)

• Mott Transition, Antiferromagnetism, and d-wave Superconductivity in Two-Dimensional Organic Conductors
• Low-energy properties of aperiodic quantum spin chains
• Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: a renormalization-group approach

Cited by in corpus (1)

• Aperiodic Ising model on the Bethe lattice: Exact results