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arxiv: 0808.3512 · v2 · submitted 2008-08-26 · ❄️ cond-mat.stat-mech

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
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(3) Laboratoire de Physique des Materiaux Nancy-Universite)
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classification ❄️ cond-mat.stat-mech
keywords aperiodiccriticalisingbehaviorbethelatticemodelanalytical
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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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