A procedure originally developed to compute the ground states of this system relies on the mathematical formula that "the natural logarithm of a variable Z" equals "the limit as n goes to zero" of "minus one plus Z to the n," all divided by "n." Giorgio Parisi used that "replica trick" to solve this system under the mean 3eld approximation.
Under the assumptions of uniformity, mutual variable independence, and paÂ·raÂ·metÂ·erÂ·ization redundancy, this system's spherically constrained Hamiltonian is equivalent to the loss function of a fully decoupled large-size neural network. A procedure originally developed to compute the ground states of this system relies on the mathematical formula that "the natural logarithm of a variable Z" equals "the limit as n goes to zero" of "minus one plus Z to the n," all divided by "n." Giorgio Parisi used that "replica trick" to solve this system under the mean 3eld approximation. This system undergoes non-exponential decay of the reÂ·maÂ·nent magnetization below its transition temperature a7ter the removal of all external magnetic 3elds. For 10 points, name this system that exhibits quenched disorder leading to geometrical frustration, and can be represented as a lattice of randomly aligned magnetic dipoles.
Under the assumptions of uniformity, mutual variable independence, and paÂ·raÂ·metÂ·erÂ·ization redundancy, this system's spherically constrained Hamiltonian is equivalent to the loss function of a fully decoupled large-size neural network.
spin glasses [or Sherrington-Kirkpatrick model; prompt on glasses or Ising model]