We consider the 2-spin spherical Sherrington–Kirkpatrick model whose disorder is given by a deformed Wigner matrix of form $$W+\lambda V$$ , where W and V random diagonal with i.i.d. entries. Assuming that density function entries decays faster than certain rate near edges its spectrum, we prove sharp phase transition limiting free energy fluctuation. In high temperature regime, fluctuation con...

The existence theorem for replica-symmetry breaking (RSB) in the transverse field Sherrington-Kirkpatrick (SK) model is extended to with a general random exchange interactions. relation between expectation value of interaction energy and Duhamel correlation function spin operators can be obtained by an approximate integration parts In addition Falk-Bruch inequality, these explicit evaluations e...

Background: This scoping review examined the outcomes of accelerated second-degree baccalaureate and master nursing programs using Kirkpatrick four-level model. Method: A systematic search four major scientific databases identified 15 articles meeting study inclusion criteria. The were assessed for educational outcomes, extracted data organized according to model consisting reaction, learning, ...

We conjecture that the Parisi functional in the Sherrington-Kirkpatrick model is convex in the functional order parameter. We prove a partial result that shows the convexity along “one-sided” directions. An interesting consequence of this result is the log-convexity of Lm norm for a class of random variables.

In [11] Michel Talagrand gave a rigorous proof of the Parisi formula in the classical Sherrington-Kirkpatrick (SK) model. In this paper we build upon the methodology developed in [11] and extend Talagrand’s result to the class of SK type models in which the spins have arbitrary prior distribution on a bounded subset of the real line.

Glauber dynamics of the Sherrington–Kirkpatrick spin-glass model in the hightemperature phase is studied using theory and computer simulations. The theoretical approach follows the spirit of Mori’s continuous fraction expansion. Its predictions agree very well with the computer simulation results.