We consider the quantum Sherrington–Kirkpatrick (SK) spin-glass model with a transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures β > 0. To characterize the free energy, we use the path integral representation of the partition function and approximate the model by a sequence of finite-dimensional vector-spin glasses with -valued spins. This enables us to use the results of Panchenko who generalized [Ann. Probab. 46(2), 829–864 (2018); ibid, 46(2), 865–896 (2018)] the Parisi formula to classical vector-spin glasses. As a consequence, we can express the thermodynamic limit of the free energy of the quantum SK model as the d → ∞ limit of the free energies of the d-dimensional approximations of the model.
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Research Article| August 27 2020
Free energy of the quantum Sherrington–Kirkpatrick spin-glass model with transverse field
Arka Adhikari ;
Arka Adhikari, Christian Brennecke; Free energy of the quantum Sherrington–Kirkpatrick spin-glass model with transverse field. J. Math. Phys. 1 August 2020; 61 (8): 083302. https://doi.org/10.1063/5.0009291
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