A spin glass is a disordered material exhibiting high magnetic frustration. The origin of the behavior can be either a disordered structure (such as that of a conventional, chemical glass) or a disordered magnetic doping in an otherwise regular structure. Frustration refers to the inability of the system to remain in a single lowest energy state (the ground state). Spin glasses have many ground states which are never explored on experimental time scales. Magnetic lines of force of a bar magnet shown by iron filings on paper In physics, magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. ... Glass can be made transparent and flat, or into other shapes and colors as shown in this sphere from the Verrerie of Brehat in Brittany. ... // The word frustration was introduced to describe the situation where a system cannot simultaneously minimize the interaction energies between its components1. ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ...

It is the time dependence which distinguishes spin glasses from other magnetic systems. Beginning above the spin glass transition temperature, T_c, where the spin glass exhibits more typical magnetic behavior, (such as paramagnetism as discussed here but other kinds of magnetism are possible), if an external magnetic field is applied and the magnetization is plotted versus temperature, it follows the typical Curie law (in which magnetization is inversely proportional to temperature) until T_c is reached, at which point the magnetization becomes virtually constant (this value is called the field cooled magnetization). This is the onset of the spin glass phase. When the external field is removed, the spin glass has a rapid decrease of magnetization to a value called the remnant magnetization, and then a slow decay as the magnetization approaches zero (or some small fraction of the original value - this remains unknown). This decay is non-exponential and no single function can fit the curve of magnetization versus time adequately. 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. In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ... Simple Illustration of a paramagnetic probe made up from miniature magnets. ... Current (I) flowing through a wire produces a magnetic field () around the wire. ... Magnetization of a paramagnet as a function of temperature. ...

If a similar procedure was followed for a ferromagnetic substance, when the external field is removed, there would be a rapid change to a remnant value, but this value is a constant in time. For a paramagnet, when the external field is removed, the magnetization rapidly goes to zero. In each case, the change is very rapid and if carefully examined it is exponential decay with a very small time constant. Ferromagnetism is a phenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetism. ...

If instead, the spin glass is cooled below T_c in the absence of an external field, and then a field is applied, there is a rapid increase to a value called the zero-field-cooled magnetization, which is less than the field cooled magnetization, followed by a slow upward drift toward the field cooled value.

Surprisingly, the sum of the two complex functions of time (the zero-field-cooled and remnant 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.

In addition to unusual experimental properties, spin glasses are the subject of extensive theoretical and computational investigation. A great deal of early theoretical work on spin-glasses uses a form of mean field theory based on a set of replicas of the partition function of the system. An influential exactly-solvable model of a spin-glass was introduced by D. Sherrington and S. Kirkpatrick, and led to considerable theoretical extensions of mean field theory to model the slow dynamics of the magnetisation, and the complex non-ergodic equilibrium state. The formalism of replica mean field theory has also been applied in the study of neural networks, where it has enabled calculations of properties such as the storage capacity of simple neural network architectures without requiring a training algorithm (such as backpropagation) to be designed or implemented. A many-body system with interactions is generally very difficult to solve exactly, except for extremely simple cases (Gaussian field theory, 1D Ising model. ... In number theory, see Partition function (number theory) In statistical mechanics, see Partition function (statistical mechanics) In quantum field theory, see Partition function (quantum field theory) In game theory, see Partition function (game theory) This is a disambiguation page — a navigational aid which lists other pages that might otherwise... A many-body system with interactions is generally very difficult to solve exactly, except for extremely simple cases (Gaussian field theory, 1D Ising model. ... A neural network is an interconnected group of neurons. ... Backpropagation is a supervised learning technique used for training artificial neural networks. ...

See also

• Quenched disorder
• Replica trick
• Cavity method
• Geometrical frustration
• Phase transition
• Ferromagnetic interaction
• Antiferromagnetic interaction
• Crystal structure

In statistical physics, a system is said to present quenched disorder when some parameters defining its behaviour are random variables which do not evolve with time, i. ... In statistical physics of spin glasses and other systems with quenched disorder, the replica trick is a mathematical technique based on the application of the formula Categories: | ... The Cavity method is a mathematical method due to M. Mezard, G. Parisi and M.A. Virasoro in 1985 to compute properties of ground states in many condensed matter and optimization problems. ... Geometrical frustration is a phenomenon in condensed matter physics in which the geometrical properties of the atomic lattice forbid the existence of a unique ground state. ... In physics, a phase transition, (or phase change) is the transformation of a thermodynamic system from one phase to another. ... A ferromagnetic interaction acts to align spins. ... An anti-ferromagnetic interaction acts to anti-align neighboring spins. ... Enargite crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ...

Magnetic lines of force of a bar magnet shown by iron filings on paper In physics, magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. ... Levitating pyrolytic carbon Diamagnetism is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field. ... Superdiamagnetism (or perfect diamagnetism) is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic susceptibility and the exclusion of the interior magnetic field. ... Simple Illustration of a paramagnetic probe made up from miniature magnets. ... Superparamagnetism is a phenomenon by which magnetic materials may exhibit a behavior similar to paramagnetism even when at temperatures below the Curie or the Néel temperature. ... Ferromagnetism is the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field. ... In materials that exhibit antiferromagnetism, the spins of magnetic electrons align in a regular pattern with neighboring spins pointing in opposite directions. ... In physics, a ferrimagnetic material is one in which the magnetic moment of the atoms on different sublattices oppose as in antiferromagnetism but the opposing moments are unequal and a spontaneous magnetization remains. ... Metamagnetism is a physical state of matter characterized by a superlinear increase of magnetization over a narrow range of applied magnetic field. ...

References

• K.H. Fischer and J.A. Hertz, Spin Glasses, Cambridge University Press (1991)
• Mezard, Marc; Giorgio Parisi, Miguel Angel Virasoro (1987). Spin glass theory and beyond. Singapore: World Scientific. ISBN 9971-5-0115-5. 
• J. A. Mydosh, Spin Glasses, Taylor & Francis (1995)
• P. Nordblad, L. Lundgren and L. Sandlund, J. Mag. and Mag. Mater. 54, pp. 185 (1986)
• S. Boettcher, Emory University
• S. I. Fullem (2006). Study of superspin-glass effect and superparamagnetic behavior in Fe₃O₄ nanoparticles and gold-coated Fe₃O₄ nanoparticles. Binghamton University (M. S. Thesis). ISBN 9780542784859. 
• Spin glass on arxiv.org