Free energy of mean-field spin-glass models: Evolution operator and perturbation expansion

Spin glass theory is extensively complicated, thus the full mean-field solution of spin glass models with a continuous order-parameter function is not directly available and approximate schemes must be used to assess its properties. The main goal is to find such solutions that wouldn't show non-physical behavior eg. negative enthropy for absolute zero. We introduced evolution operator applicable to the whole range of temperatures while simultaneously suppressing non-physical behavior even in the lowest evolution order.

Temperature dependence of entropy (left) calculated in 1RSB, with first correction to it, and the replica-symmetric solution. Free energy (right) of the SK solution (fSK), 1RSB (f₀), and the first correction to 1RSB (f₁)

¹Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, Praha, Czech Republic