Model spin glass

While the locations of the spins are not random - indeed, the spins populate sites of a regular lattice - the interactions themselves are completely random. Frustration, too, has been retained. Thus, arguably, two of the three fundamental properties of real spin glass systems are satisfied. What remains to be seen, of course, is the extent to which this simplified model retains the overall physics. 

Derrida and Flyvberg [flyvb88] and Derrida and Bessis [derrida88] have examined the overlap between two attractors by looking at the probability that two randomly chosen initial state.s evolve toward the same attractor. These studies find that the distribution is very similar to that found in certain spin-glass models. 

The frustration effects are implicit in many physical systems, as different as spin glass magnets, adsorbed monomolecular films and liquid crystals [32, 54, 55], In the case of polar mesogens the dipolar frustrations may be modelled by a spin system on a triangular lattice (Fig, 5), The corresponding Hamiltonian consists of a two particle dipolar potential that has competing parallel dipole and antiparallel dipole interactions [321, The system is analyzed in terms of dimers and trimers of dipoles. When the dipolar forces between two of them cancel, the third dipole experiences no overall interaction. It is free to permeate out of the layer, thus frustrating smectic order. 

This nanoparticle sample exhibits strong anisotropy, due to the uniaxial anisotropy of the individual particles and the anisotropic dipolar interaction. The relative timescales (f/xm) of the experiments on nanoparticle systems are shorter than for conventional spin glasses, due to the larger microscopic flip time. The nonequilibrium phenomena observed here are indeed rather similar to those observed in numerical simulations on the Ising EA model [125,126], which are made on much shorter time (length) scales than experiments on ordinary spin glasses [127]. 

The concept of a nonequilibrium temperature has stimulated a lot of research in the area of glasses. This line of research has been promoted by Cugliandolo and Kurchan in the study of mean-held models of spin glasses [161, 162] that show violations of the fluctuation-dissipation theorem (FDT) in the NEAS. The main result in the theory is that two-time correlations C t,t ) and responses R t, f ) satisfy a modihed version of the FDT. It is customary to introduce the effective temperature through the fluctuation-dissipation ratio (FDR) [163] dehned as... 

L. F. Cugliandolo and J. Kurchan, Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model. Phys. Rev. Lett. 71, 173-176 (1993). 

E. Marinari, G. Parisi, and F Ritort, Replica field theory for deterministic models. II. A non-random spin glass with glassy behaviour. J. Phys. A 27, 7647—7668 (1994). 

D. Sherrington and A. Kirlq)atrick, Solvable model of a spin-glass. Phys. Rev. Lett. 35, 1792-1796 (1975). 

Interaction frustration has also been found to be a control parameter for fragility in a spin model of glass formation. 

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