The energy of a Hopfield neural network is calculated by noting that the network is equivalent to it. Formulated in matrix terms, the log of its largest eigenvalue is proportional to the free energy. Using a Metropolis algorithm with staying probability e to the negative beta times delta E can be used to solve these models. Istrail found that the three-dimensional versions of them are unsolvable. The energy in this system is equal to the sum of S sub I times S sub J times an interaction term J sub ij. A 2-dimensional version of it was solved by Onsager. Sherrington and Kirkpatrick added frustration terms to it in order to model spin glasses. 
The energy of a Hopfield neural network is calculated by noting that the network is equivalent to it. Formulated in matrix terms, the log of its largest eigenvalue is proportional to the free energy. Using a Metropolis algorithm with staying probability e to the negative beta times delta E can be used to solve these models. Istrail found that the three-dimensional versions of them are unsolvable. The energy in this system is equal to the sum of S sub I times S sub J times an interaction term J sub ij. A 2-dimensional version of it was solved by Onsager. Sherrington and Kirkpatrick added frustration terms to it in order to model spin glasses. Its critical fluctuations correctly model the behavior at the critical point. For 10 points, name this model which is used to model magnetic materials as a collection of spins.
The energy of a Hopfield neural network is calculated by noting that the network is equivalent to it.
 the Ising model