Citation
Abstract
This paper finds a rigorous asymptotic expression for the number of stable points of an infinite-range spin glass with independently identically distributed (i.i.d.) zero-mean gaussian exchange interactions. The result also applies to the number of stable points of a Hopfield Memory (a kind of associative memory) when the memory connections are i.i.d. zero-mean gaussians. The result is that the number of stable points is asymptotic to a constant slightly larger than I times 2 to a power slightly larger than n/4, where n is the number of spins in the glass, or the length of the n-tuples to be remembered by the memory. The answer is easily derived using simple asymptotic techniques from an exact expression for the probability that an arbitrary +1 n-tuple of spins is a fixed point. This expression is obtained from the fact that any distribution of joint zero-mean gaussians of given covariances is specified solely by these covariances. This is a far shorter derivation of the result than those existing.
Details
- Volume
- 42-83
- Published
- November 15, 1985
- Pages
- 209–215
- File Size
- 327.6 KB