Vanishing Critical Magnetization in the Quantum Ising Model

Journal article, 2015

Adapting the recent argument of Aizenman, Duminil-Copin and Sidoravicius for the classical Ising model, it is shown here that the magnetization in the transverse-field Ising model vanishes at the critical point. The proof applies to the ground state in dimension d a parts per thousand yen 2 and to positive-temperature states in dimension d a parts per thousand yen 3, and relies on graphical representations as well as an infrared bound.