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Aperiodic Ising model on the Bethe lattice: exact results
1Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary. igloi@szfki.hu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
We analyzed the Ising model with aperiodic couplings on the Bethe lattice. Our study provides an exact solution for critical behavior in marginal aperiodic sequences, revealing continuously varying critical exponents.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Complex systems
Background:
- The Ising model is a fundamental model in statistical mechanics.
- Aperiodic systems exhibit complex behaviors not seen in periodic systems.
- Previous numerical studies explored the Ising model on the Bethe lattice with aperiodic couplings.
Purpose of the Study:
- To present a relevance-irrelevance criterion for aperiodic Ising models.
- To solve the critical behavior exactly for marginal aperiodic sequences.
- To derive analytical formulas for continuously varying critical exponents.
Main Methods:
- Exact solution of the Ising model on the Bethe lattice.
- Analysis of aperiodic modulation of couplings.
- Development of a relevance-irrelevance criterion.
Main Results:
- Exact solution for critical behavior in marginal aperiodic sequences.
- Analytical formulas for continuously varying critical exponents.
- Identification of a relationship with the critical behavior of aperiodic quantum Ising chains.
Conclusions:
- The study provides an exact analytical framework for understanding critical phenomena in aperiodic systems.
- The findings offer insights into the universality and scaling properties of complex magnetic systems.
- The work establishes a connection between classical and quantum aperiodic Ising models.
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