2012/03/10 by W. N. Yessen, Yessen, W. N.
Mathematics · Physics and Astronomy · #82B10 #82B26 #82B27 #82B44 #82D30 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 82B20 #Secondary: 82D40 #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP #msc:82B10 #msc:82B20 #msc:82B26 #msc:82B27 #msc:82B44 #msc:82D30 #msc:82D40
paper · pdf · doi:10.48550/arxiv.1203.2221
32 pages, 87 references. Final version. To appear in Annal. H. Poincare
arxiv created 2013/04/10 · arxiv updated 2013/04/11
In this paper we consider one-dimensional classical and quantum spin-1=2 quasiperiodic Ising chains, with two-valued nearest neighbor interaction modulated by a Fibonacci substitution sequence on two letters. In the quantum case, we investigate the energy spectrum of the Ising Hamiltonian, in presence of constant transverse magnetic field, by employing the techniques that were developed in our previous work. In the classical case, we investigate and prove analyticity of the free energy function when the magnetic field, together with interaction strength couplings, is modulated by the same Fibonacci substitution (thus proving absence of phase transitions of any order at finite temperature). We also investigate the distribution of Lee-Yang zeros of the partition function in the complex magnetic field regime, and prove its Cantor set structure (together with some additional qualitative properties), thus providing a rigorous justification for the observations in some previous works. In both, quantum and classical models, we concentrate on the ferromagnetic class.