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

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.

12 pages, 7 figures

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Cited by in corpus (3)

• The phase transition of the quantum Ising model is sharp
• Graphical representations of Ising and Potts models
• Critical behavior of models with infinite disorder at a star junction of chains