Spin glasses

Site-disorder, bond disorder and quantum spin glasses

 

Site-disorder

Spin glasses are the magnetic analog of real glasses. They contain magnetic elements that can be ordered in a new fashion, the spin glass phase. The best know example is a Au_(1-c)Fe_c, e.g. golden ring with, say c=2% of iron in it; at a low enough temperature, a few Kelvin, this system exhibits a new kind of ordering, the spin glass order, with new properties, like very long relaxation times and hysteresis.

For this system the famous problem of site-disorder, typically present in practice, was solved [L10]. This explained the linear relation between transition temperature and concentration in metallic spin glasses at small concentrations, and allowed to describe its powerlaw continuation [L46] at concentrations up to some 10-15%, as well as the cluster glass phase [L28], [P48] for still larger concentrations. The latter two works were done with undergraduate student Coen van Duin.

[L46] R. Serral Gracia, Th. M. N, and I. V. Lerner, Concentration dependence of the transition temperature in metallic spin glasses, Europhys. Lett. 66 (2004) 419-422

[P48] Th.M. N. and C.N.A. van Duin, Theory of site-disordered magnets,
Eur. Phys. J. B 7 (1999) 191-209

[L28] Th.M. N. and C.N.A. van Duin, Ginzburg-Landau theory of the cluster glass phase,
J. Phys. A 30 (1997) L55-L61

[L19] Th.M. N., Field theory for site-disordered spin glasses, Europhys. Lett. 24 (1993) 797-802

 

Bond disorder

The more common approach involves bond-disordered spin glasses. In [L25] a special model is described, where the Parisi overlap function can be calculated analytically, in a back-to-back publication about a new definition of spherical spins, [L26], see also [P64].
Also a number of other questions in this field were considered.

[P64] R. Serral Gracia, Th.M. N., Quantum spherical spin models, Phys. Rev. E (2004)

[P50] A.E. Allahverdyan, Th.M. N., and D.B. Saakian, Model glasses coupled to two different heat baths, Eur. Phys. J. B 16 (2000) 317-355

[L34] J. Hertz, D. Sherrington and Th. M. N., Competition between glassiness and order in a multi-spin glass, Phys. Rev. E 60 (1999) 2460-2463 (Brief Reports)

[P42] D.B. Saakian and Th.M. N., Variational approach to interfaces in random media: negative variances and replica symmetry breaking, J. de Physique I France 7 (1997) 1513-1521

[P37] Th. M. N., A puzzle on fluctuations of weights in spin glasses, J. de Physique I France 6 (1996) 109-117

[L26] Th.M. N., Quantum description of spherical spins, Phys. Rev. Lett. 74 (1995) 4293-4296

[L25] Th.M. N., Exactly solvable model of a quantum spin glass, Phys. Rev. Lett. 74 (1995) 4289-4292

[L2] Th.M. N., Spherical spin glass with short range ferromagnetic interactions, Phys. Rev. B 31 (1985) 7487-7490

 

Quantum spin glasses

Spin glasses loose their ordering at low temperatures when they are subject to a transversal field, as this tries to direct them in the perpendicular plane. Such systems are called quantum spinglasses, see [P43]. They exhibit specific quantum properties.

[P43] Th.M. N. and F. Ritort, Quantum phase transition in spin glasses with multi-spin interactions, Physica A 250, (1998) 8-45