99-14 Barbara Gentz, Matthias Loewe

Fluctuations in the Hopfield Model at the critical temperature (332K, Postscript) Jan 12, 99

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We investigate the fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks at the critical temperature $1/\beta_c=1$. The number of patterns $M(N)$ is allowed to grow with the number $N$ of spins but the growth rate is subject to the constraint $M(N)^{15}/N\to 0$. As the system size $N$ increases, on a set of large probability the distribution of the appropriately scaled order parameter under the Gibbs measure comes arbitrarily close (in a metric which generates the weak topology) to a non-Gaussian measure which depends on the realization of the random patterns. This random measure is given explicitly by its (random) density.

Files: 99-14.src( 99-14.comments , 99-14.keywords , critical_fluctuations.ps )