Quantum Ising Quasi-Crystal

Abstract

A quantum Ising spin chain with two-valued nearest-neighbour couplings arranged in a quasi-periodic sequence is considered, in the presence of a uniform transverse field. The scaling properties of the energy spectrum of the model are analytically determined. The system can undergo a phase transition both when the two couplings have equal sign (ferro- or antiferromagnetic couplings) and when they have opposite sign (frustrated system). The critical point is explicitly obtained; the critical behaviour is shown to be the same as in the periodic case.