PHASE-TRANSITION IN APERIODIC QUANTUM ISING-MODELS

Phase transition in the aperiodic quantum Ising models were studied, in which the transverse magnetic fields are uniform and the couplings are arranged according to the aperiodic sequences that are generated by two types of two-tile inflation rules with initial condition {A(p)B(q)}: A --> A' = A(m11)B(m12), B --> B' = A(m21)B(m22), m12, m21 not-equal 0 and A --> A' = A(m11)B(m12), B --> B' = B(m21)A(m22), m12, m22 not-equal 0. When the inflation rules have the Pisot-Vijayaraghavan (PV) property in number theory, the generated aperiodic systems undergo phase transition at the critical points. When the inflation rules do not have the PV property, it is found that only by changing the initial conditions, the inflation rules can produce aperiodic systems exhibiting phase transition as well as aperiodic systems which do not exhibit any phase transition.