The SK model is infinite step replica symmetry breaking at zero temperature
Abstract
We prove that the Parisi measure of the mixed pspin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the SherringtonKirkpatrick 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:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.06872
 Bibcode:
 2017arXiv170306872A
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 revised version