The distribution of the partition function of the Hopfield model with finite number of patterns

Abstract

We derive the leading term in the large-N asymptotic expansion of the partition function of the Hopfield model with finite number of patterns. We show that this leading-order term is deterministic in the high-temperature region. In the low-temperature region and at the critical point it is random with the distribution governed by chi(2), normal, or iterated exponential distributions.