Aperiodic Ising model on the Bethe lattice: Exact results
F. Igloi (1,2,3), L. Turban (3) ((1) Research Institute for Solid, State Physics, Optics, Budapest, (2) Institute of Theoretical Physics,, Szeged University, (3) Laboratoire de Physique des Materiaux,, Nancy-Universite)
TL;DR
This paper provides an exact analytical study of the critical behavior of the Ising model on the Bethe lattice with aperiodic couplings, including a criterion for relevance and explicit critical exponents, linking to quantum chain behavior.
Contribution
It introduces a relevance-irrelevance criterion and derives exact formulas for critical exponents in the aperiodic Ising model on the Bethe lattice.
Findings
Derived exact critical exponents for marginal aperiodic sequences.
Established a criterion to determine the relevance of aperiodic modulations.
Linked the critical behavior to that of the aperiodic quantum Ising chain.
Abstract
We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical behavior exactly for marginal aperiodic sequences. We present analytical formulae for the continuously varying critical exponents and discuss a relationship with the (surface) critical behavior of the aperiodic quantum Ising chain.
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