Critical Value of the Quantum Ising Model on Star-Like Graphs

TL;DR

This paper rigorously determines the critical value of the ground-state quantum Ising model in a transverse field on star-like planar graphs using graphical and probabilistic methods.

Contribution

It introduces a method to find the critical point of the quantum Ising model on star-like graphs via FK-representation and geometric tools.

Findings

Critical value determined for quantum Ising model on star-like graphs

Method applicable to a class of planar graphs including star graphs

Uses graphical FK-representation and probabilistic techniques

Abstract

We present a rigorous determination of the critical value of the ground-state quantum Ising model in a transverse field, on a class of planar graphs which we call star-like. These include the star graph, which is a junction of several copies of Z at a single point. Our approach is to use the graphical, or FK-, representation of the model, and the probabilistic and geometric tools associated with it.