Phase Transitions in Disordered Quantum Systems: Transverse Ising Models

  • Bikas K. Chakrabarti
  • Arnab Das
Chapter
Part of the Texts and Readings in Physical Sciences book series (volume 11)

Abstract

We introduce the transverse Ising model as a prototype for discussing quantum phase transitions. Mean field theory and its application to superconductivity by BCS are discussed, as well as real space renormalization group techniques in one dimension. Next, we introduce the Suzuki-Trotter formalism to show the correspondence between d-dimensional quantum systems and (d + 1)-dimensional classical systems. We then discuss transverse Ising spin glass models, namely the Sherrington-Kirkpatrick (SK) model, the Edwards-Anderson (EA) model and the ±J model. We briefly discuss the mean field, exact diagonalization and quantum Monte Carlo results for their phase diagrams. We discuss the question of replica symmetry restoration in quantum spin glasses due to the possibility of tunneling through the barriers. Finally, we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses.

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Copyright information

© Hindustan Book Agency 2012

Authors and Affiliations

  • Bikas K. Chakrabarti
  • Arnab Das

There are no affiliations available

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