The SK model is infinite step replica symmetry breaking at zero temperature
Abstract
We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2017
- DOI:
- 10.48550/arXiv.1703.06872
- arXiv:
- arXiv:1703.06872
- Bibcode:
- 2017arXiv170306872A
- Keywords:
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- Mathematics - Probability;
- Mathematical Physics
- E-Print:
- revised version