Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice

TL;DR

This study uses Quantum Monte Carlo simulations to explore Griffiths singularities in a site-diluted 2D transverse field Ising model, revealing different Griffiths phase behaviors at varying transverse fields.

Contribution

It provides the first detailed phase diagram and analysis of Griffiths phases in the diluted 2D transverse field Ising model using quantum Monte Carlo methods.

Findings

The phase diagram varies with concentration and transverse field.

The nature of the Griffiths phase differs at small and large Gamma.

Distribution of local susceptibility characterizes Griffiths singularities.

Abstract

The site-diluted transverse field Ising model in two dimensions is studied with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the transverse field (Gamma) and temperature (T) plane for various (fixed) concentrations (p). The nature of the quantum Griffiths phase at zero temperature is investigated by calculating the distribution of the local zero-frequency susceptibility. It is pointed out that the nature of the Griffiths phase is different for small and large Gamma.