Griffiths-McCoy Singularities in the Dilute Transverse-Field Ising Model: A Numerical Linked Cluster Expansion Study

Abstract

We use Numerical Linked Cluster Expansions (NLCE) 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 (GM) singularities. We find that the magnetization develops non-linearities in the Griffiths phase with exponents that vary continuously with $h$. Additionally, the probability distribution of the local susceptibility develops long tails in the Griffith's phase, which is studied in terms of its moments.