TRACE MAPS, INVARIANTS, AND SOME OF THEIR APPLICATIONS

DOI10.1142/S021797929300247XzbMath0799.22011arXivmath-ph/9904025OpenAlexW2039578173MaRDI QIDQ4299811

Dieter Joseph, Michael Baake, Uwe Grimm

Publication date: 21 November 1994

Published in: International Journal of Modern Physics B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/9904025

zbMATH Keywords

invariantsIsing modeltransfer matricesFricke charactergap-labelling theoremgeneralized Fibonacci chainskicked two-level systems

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50)

Related Items

Reversing \(k\)-symmetries in dynamical systems ⋮ On the entropy and letter frequencies of powerfree words ⋮ Trace maps as 3D reversible dynamical systems with an invariant ⋮ Nonperiodic Ising quantum chains and conformal invariance ⋮ On the Concept of Integrability for Discrete Dynamical Systems. Investigation of Wandering Points of Some Trace Map. ⋮ Spectral analysis of tridiagonal Fibonacci Hamiltonians ⋮ Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian ⋮ Excitations in one dimension: A geometrical view of the transfer matrix method ⋮ Properties of 1D classical and quantum Ising models: rigorous results ⋮ On the spectrum of 1D quantum Ising quasicrystal ⋮ On the role of invariants for the parameter estimation problem in Hamiltonian systems ⋮ Curves of period two points for trace maps ⋮ Minimum-dimension trace maps for substitution sequences ⋮ Substitution Hamiltonians with bounded trace map orbits ⋮ Partition function zeros for aperiodic systems.