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

TL;DR

This paper investigates how aperiodic interactions in a mean-field Ising model on a Bethe lattice affect critical behavior, revealing non-universal critical exponents depending on the sequence type.

Contribution

It introduces new algorithms for generating aperiodic sequences and demonstrates that mean-field approximations can produce nonclassical critical exponents.

Findings

Fibonacci sequence yields classical critical exponents.

Period-doubling sequence results in non-universal exponents.

Relations between critical exponents hold within error margins.

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.