Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution

SERGIO CANNAS; DANIEL STARIOLO; MARIANELA CARUBELLI, ORLANDO BILLONI, SANTIAGO PIGHIN, SERGIO CANNAS, DANIEL STARIOLO, FRANCISCO TAMARIT

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2001 vol. 294 p. 362 - 374

0378-4371

We solve the Langevin dynamics of d-dimensional ferromagnetic spherical models with interactions that decay with distance as r−(d+) . The long time dynamics of correlations and responses are studied in detail in the di3erent dynamical regimes and the validity of 4uctuation?dissipation relations (or its violation) are shown. In particular, we show that the 4uctuation?dissipation ratio X (t + tw; tw) is asymptotically a function only of the waiting time tw inthe aging regime and that X →0 as tw →∞. The results are valid in any 6nite dimension d and for 0¡¡2 where short-range behavior is recovered. We also solve the T = 0 Cahn?Hilliard dynamics of this model (conserved order parameter). An analysis of the multiscaling behavior of the autocorrelationfunctionis presented