Critical Value of the Quantum Ising Model on Star-Like Graphs |
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Authors: | Jakob?E?Bj?rnberg |
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Institution: | (1) University of Cambridge, Cambridge, UK;(2) Royal Institute of Technology, Stockholm, Sweden |
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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 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.
This research was carried out during the author’s Ph.D. studentship at the University of Cambridge, UK, and the Royal Institute
of Technology (KTH), Sweden. The author gratefully acknowledges funding from KTH during this period. The author would also
like to thank Riddarhuset, Stockholm, for generous support during his studies. |
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Keywords: | Ising model Random-cluster model Critical value |
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