We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
Bibliographical noteFunding Information:
W.-K. C. thanks Giorgio Parisi for valuable suggestions and Wenqing Hu for fruitful discussions at the early stage of this work. Both authors thank the 2016 emphasis year in probability at Northwestern University, where this work was discussed. Supported in part by NSF Grant DMS-15-97864. Supported in part by NSF Grant DMS-16-42207 and Hong Kong Research Grants Council GRF-14302515.
Received June 2016; revised December 2016. 1Supported in part by NSF Grant DMS-15-97864. 2Supported in part by NSF Grant DMS-16-42207 and Hong Kong Research Grants Council GRF-14302515. MSC2010 subject classifications. 60K35. Key words and phrases. Spin glasses, ground state energy, Parisi formula.
© Institute of Mathematical Statistics, 2017.
- Ground state energy
- Parisi formula
- Spin glasses