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Journal of Statistical Physics

, Volume 135, Issue 3, pp 571–583 | Cite as

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

  • Jakob E. Björnberg
Article

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.

Keywords

Ising model Random-cluster model Critical value 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of CambridgeCambridgeUK
  2. 2.Royal Institute of TechnologyStockholmSweden

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