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Spin glass

A spin glass is a disordered magnet with frustrated interactions, augmented by stochastic positions of the spins, where conflicting interactions, namely both ferromagnetic and also antiferromagnetic bonds, are randomly distributed with comparable frequency. The term "glass" comes from an analogy between the magnetic disorder in a spin glass and the positional disorder of a conventional, chemical glass, e.g., a window glass. Spin glasses display many metastable structures leading to a plenitude of time scales which are difficult to explore experimentally or in simulations.It is the time dependence which distinguishes spin glasses from other magnetic systems. Above the spin glass transition temperature, Tc,[note 1] the spin glass exhibits typical magnetic behaviour (such as paramagnetism). If a magnetic field is applied as the sample is cooled to the transition temperature, magnetization of the sample increases as described by the Curie law. Upon reaching Tc, the sample becomes a spin glass and further cooling results in little change in magnetization. This is referred to as the field-cooled magnetization. When the external magnetic field is removed, the magnetization of the spin glass falls rapidly to a lower value known as the remanent magnetization. Magnetization then decays slowly as it approaches zero (or some small fraction of the original value—this remains unknown). This decay is non-exponential and no simple function can fit the curve of magnetization versus time adequately.{{[J. Phys.: Condens. Matter 10 (1998) 11049–11054. Printed in the UK]BB} This slow decay is particular to spin glasses. Experimental measurements on the order of days have shown continual changes above the noise level of instrumentation.{{[J. Phys.: Condens. Matter 10 (1998) 11049–11054. Printed in the UK. BB]}} Spin glasses differ from ferromagnetic materials by the fact that after the external magnetic field is removed from a ferromagnetic substance, the magnetization remains indefinitely at the remanent value. Paramagnetic materials differ from spin glasses by the fact that, after the external magnetic field is removed, the magnetization rapidly falls to zero, with no remanent magnetization. In each case the decay is rapid and exponential.[citation needed] If the sample is cooled below Tc in the absence of an external magnetic field and a magnetic field is applied after the transition to the spin glass phase, there is a rapid initial increase to a value called the zero-field-cooled magnetization. A slow upward drift then occurs toward the field-cooled magnetization. Surprisingly, the sum of the two complex functions of time (the zero-field-cooled and remanent magnetizations) is a constant, namely the field-cooled value, and thus both share identical functional forms with time (Nordblad et al.), at least in the limit of very small external fields.

 
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