Quasiperiodicity and long-range order in a magnetic system

Abstract

We study the 1D quasiperiodic quantum Ising model in a transverse field, which exhibits long-range order above a critical coupling and describes the phase diagram of the 2D classical Ising-model quasiperiodic in one direction. We numerically determine the correlation length, magnetization, and energy spectrum of this system. The site dependency of the magnetization is described by a new order parameter, the width of the magnetization. The scalings δ and f(α) associated with the Cantor spectrum are found to exhibit special features at the onset of long-range order.