The Aizenman-Sims-Starr and Guerras schemes for the SK model with multidimensional spins

Anton Bovier, Anton Klimovsky
2009 Electronic Journal of Probability  
We prove upper and lower bounds on the free energy of the Sherrington-Kirkpatrick model with multidimensional spins in terms of variational inequalities. The bounds are based on a multidimensional extension of the Parisi functional. We generalise and unify the comparison scheme of Aizenman, Sims and Starr and the one of Guerra involving the GREM-inspired processes and Ruelle's probability cascades. For this purpose, an abstract quenched large deviations principle *
doi:10.1214/ejp.v14-611 fatcat:5xt3w56aobcrtbrchhtp4wtu5e