Aperiodic Ising model on the Bethe lattice: Exact results
arXiv:0808.3512 · doi:10.1103/PhysRevE.78.031128
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.
7 pages, 3 figures, minor corrections
References in corpus (11)
- Aperiodic Ising Quantum Chains
- Low-energy properties of aperiodic quantum spin chains
- Surface Magnetization and Critical Behavior of Aperiodic Ising Quantum Chains
- Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
- Relevant Aperiodic Modulation in the 2d Ising Model
- Surface Magnetization of Aperiodic Ising Systems: a Comparative Study of the Bond and Site Problems
- Anisotropic Scaling in Layered Aperiodic Ising Systems
- Marginal Anisotropy in Layered Aperiodic Ising Systems
- Surface Properties of Aperiodic Ising Quantum Chains
- Aperiodic spin chain in the mean-field approximation
- Non-universal behavior for aperiodic interactions within a mean-field approximation
Cited by in corpus (3)
- Strong-disorder renormalization group study of the Anderson localization transition in three and higher dimensions
- Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
- Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model