Editing Spin glass (section)

==Magnetic behavior==
{{See also|Amorphous magnet}}
It is the time dependence which distinguishes spin glasses from other magnetic systems.

Above the spin glass [[phase transition|transition temperature]], ''T''<sub>c</sub>,<ref group="note"><math>T_\text{c}</math> is identical to the so-called "freezing temperature" <math>T_\text{f}.</math></ref> the spin glass exhibits typical magnetic behaviour (such as [[paramagnetism]]).

If a [[applied magnetic field|magnetic field]] is applied as the sample is cooled to the transition temperature, magnetization of the sample increases as described by the [[Curie's law|Curie law]]. Upon reaching ''T''<sub>c</sub>, 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{{snd}} this [[List of unsolved problems in physics|remains unknown]]). This [[exponential decay|decay is non-exponential]], and no simple function can fit the curve of magnetization versus time adequately.<ref name="JPhys">{{cite journal |last1=Joy |first1=P. A. |last2=Kumar |first2=P. S. Anil |last3=Date |first3=S. K. |title=The relationship between field-cooled and zero-field-cooled susceptibilities of some ordered magnetic systems |journal=J. Phys.: Condens. Matter |date=7 October 1998 |volume=10 |issue=48 |pages=11049–11054 |doi=10.1088/0953-8984/10/48/024 |bibcode=1998JPCM...1011049J |s2cid=250734239 }}</ref> 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.{{r|JPhys}}

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. The decay is rapid and exponential.{{Citation needed|date=September 2011}}

If the sample is cooled below ''T''<sub>c</sub> 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 complicated 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,<ref name="Nordblad">{{cite journal |last1=Nordblad |first1=P. |last2=Lundgren |first2=L. |last3=Sandlund |first3=L. |title=A link between the relaxation of the zero field cooled and the thermoremanent magnetizations in spin glasses |journal=Journal of Magnetism and Magnetic Materials |date=February 1986 |volume=54–57 |issue=1 |pages=185–186 |doi=10.1016/0304-8853(86)90543-3 |bibcode=1986JMMM...54..185N }}</ref> at least in the limit of very small external fields.