The Free Energy of a Quantum Sherrington–Kirkpatrick Spin-Glass Model for Weak Disorder

@article{Leschke2019TheFE,
  title={The Free Energy of a Quantum Sherrington–Kirkpatrick Spin-Glass Model for Weak Disorder},
  author={Hajo Leschke and Sebastian Rothlauf and Rainer Ruder and Wolfgang L. Spitzer},
  journal={Journal of Statistical Physics},
  year={2019}
}
<jats:p>We extend two rigorous results of <jats:sc>Aizenman</jats:sc>, <jats:sc>Lebowitz</jats:sc>, and <jats:sc>Ruelle</jats:sc> in their pioneering paper of 1987 on the <jats:sc>Sherrington</jats:sc>–<jats:sc>Kirkpatrick</jats:sc> spin-glass model without external magnetic field to the quantum case with a “transverse field” of strength <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathsf {b}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML… 
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Existence of Replica-Symmetry Breaking in Quantum Glasses.
By controlling quantum fluctuations via the Falk-Bruch inequality we give the first rigorous argument for the existence of a spin-glass phase in the quantum Sherrington-Kirkpatrick model with a
Phase Diagram of the Quantum Random Energy Model
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We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures
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TLDR
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