Griffiths-McCoy singularities in the dilute transverse-field Ising model: A numerical linked cluster expansion study.

We use numerical linked cluster expansions (NLCEs) to study the site-diluted transverse-field Ising model on the square lattice at T=0. NLCE with a self-consistent mean field on the boundary of the clusters is used to obtain the ground-state magnetization, susceptibility, and structure factor as a function of transverse field h and exchange constant J. Adding site dilution to the model turns NLCE into a series expansion in the dilution parameter p. Studying the divergence of the structure factor allows us to establish the phase diagram in the h/J and p plane. By studying the magnetization of the system in a longitudinal field, we investigate the Griffiths-McCoy singularities. We find that the magnetization develops nonlinearities in the Griffiths phase with exponents that vary continuously with h. Additionally, the probability distribution of the local susceptibility develops long tails in the Griffiths phase, which is studied in terms of its moments.