| Автор | I Pérez Castillo |
| Автор | N S Skantzos |
| Дата выпуска | 2004-10-01 |
| dc.description | We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little–Hopfield model). We solve this model within replica symmetry, and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetic transition lines of our phase diagram are identical to those of sequential dynamics. The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Копирайт | 2004 IOP Publishing Ltd |
| Название | The Little–Hopfield model on a sparse random graph |
| Тип | paper |
| DOI | 10.1088/0305-4470/37/39/003 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 37 |
| Первая страница | 9087 |
| Последняя страница | 9099 |
| Аффилиация | I Pérez Castillo; Institute for Theoretical Physics, Celestijnenlaan 200D, Katholieke Universiteit Leuven, Leuven B-3001, Belgium |
| Аффилиация | N S Skantzos; Institute for Theoretical Physics, Celestijnenlaan 200D, Katholieke Universiteit Leuven, Leuven B-3001, Belgium |
| Выпуск | 39 |
