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- Department of Economics,
- School of Social Science
- City University,
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- London EC1V 0HB.

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The effects of queched disorder on systems with continuous symmetry has attracted a lot of the- oretical and experimental interest. In collaboration with H. Orland and T. Garel we applied a disorder-dependent gaussian varational approach to the d-dimentional ferromagnetic X-Y model in a random field. One ma jor advantage of this approach is that it is genuinely variational, thus providing a true upper bond to the free energy of the system. We define the variational hamil- tonian and calculate the corresponding variational free energy. We discuss the issue of long-range order as a function of space dimension and find long-range ferromagnetic order at low temperature in dimension (d > 4). The randomness yelds a non extensive contribution to the variational free energy, implying a random mass term in the correlation functions. We discuss the nonextensive corrections to the free energy and study the stability of the variational solutions. The physical pictures that emerges at d < 4 is that of a marginally stable mixture of domains. We also calculate the disorder-dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size. In collaboration with E. Marinari we studied the dynamics of the SK model modified by a small non-Hamiltonian perturbation. The main question is if the complex dynamical behaviour of the SK model (aging, slow power-like decay and related effetcs) is stable under a small non-Hamiltonian perturbation. We found that, on the time scales investigated by our numerical simulations, aging survives a small perturbation (and is destroyed by a large one). If we assume that we are observing a transient behaviour, the scaling of correlation times versus the asymmetry strength is not compatible with the one expected for the spherical model. We discussed the slow power-law decay of observable quantities (Energy and q2 ) to equilibrium, and we showed that for small perturbations power-like decay is preserved. We also discussed the asymptotically large time region on small lattices. We have found, for small perturbations, very similar results to the ones of the pure model. Nonetheless for larger perturbations small lattices produce fake double peak structures that disappear in the infinite volume limit. The same effect could make trivial the theory with small perturbation on very large volume, but we could not observe such effect up to sizes investigated.

*G. Iori, J. Ortin, L. Carrillo*

Linearly driven Random Field Ising Model: hysteresis and avalanches

Anales de Fisica, 4, 245-246 (1997)*T.Garel, G.Iori. H.Orland*

A variational study of the random-field XY model

Phys. Rev. B, Vol 53, No. 6, R2941-R2944 (1996)*G. Iori, J. Ortin, L. Carrillo*

Linearly driven Random Field Ising Model: hysteresis and avalanches

Anales de Fisica, 4, 245-246 (1997)*T.Garel, G.Iori. H.Orland*

A variational study of the random-field XY model

Phys. Rev. B, Vol 53, No. 6, R2941-R2944 (1996)