We develop a very simple method to study the high temperature, or equivalently high external field, behavior of the Sherrington-Kirkpatrick mean field spin glass model. The basic idea is to couple two different replicas with a quadratic term, trying to push out the two replica overlap from its replica symmetric value. In the case of zero external field, our results reproduce the well known vali...

In 1894, in the first volume of Psychological Review, E. A. Kirkpatrick performed “an experimental study of memory,” in which he showed that items presented as visual objects are better remembered than are words and that imagery aids retention of verbal materials. Those features of his paper have been cited, off and on, throughout the years. However, toward the end of the paper, Kirkpatrick rep...

We consider the Hopfield model of size N and with p ∼ tN patterns, in the whole high temperature (paramagnetic) region. Our result is that the partition function has log-normal fluctuations. It is obtained by extending to the present model the method of the interpolating Brownian Motions used in [10] for the Sherrington-Kirkpatrick model. We view the load t of the memory as a dynamical paramete...

We study for random quantum spin systems the energy gap between the ground and first excited states to clarify a relation to the spin-glass–paramagnetic phase transition. We find that for the transverse Sherrington-Kirkpatrick model the vanishing of the averaged gap does not identify the transition. A power-law form of the gap distribution function leads to power-law distributions of the linear...

We study hysteretic phenomena in random ferromagnets. We argue that the angle dependent magnetostatic (dipolar) terms introduce frustration and long-range interactions in these systems. This makes it plausible that the Sherrington-Kirkpatrick (SK) model may be able to capture some of the relevant physics of these systems. We use scaling arguments, replica calculations, and large scale numerical...

We prove the property of stochastic stability previously introduced as a consequence of the (unproved) continuity hypothesis in the temperature of the spin-glass quenched state. We show that stochastic stability holds in β-average for both the Sherrington-Kirkpatrick model in terms of the square of the overlap function and for the Edwards-Anderson model in terms of the bond overlap. We show tha...

We present multi-column text region identification support for Ocular, the unsupervised historical printed document transcription project of Berg-Kirkpatrick et. al (2013). We use structured prediction with rich features defined on the input document and incorporate a transition model based on prior document layout assumptions. Our model is trained using a structured-SVM objective on a randomly...