Spin glass

Spin glass

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 is the inability of the system to remain in a single lowest energy state (the ground state). The typical origin of this property is the simultaneous presence of "competing interactions" and "disorder".

Spin glasses have many ground states which are never explored on experimental time scales.

Magnetic behaviour

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.

If a similar test is run on a ferromagnetic substance, when the external field is removed, there is a rapid change to a remnant value that then stays constant in time. For a paramagnet, when the external field is removed, the magnetization rapidly goes to zero and stays there. In each case the change is rapid and, if carefully examined, is found to be exponential decay with a very small time constant.

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.

History of Research

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 equilibrium solution of the model, after some early attempts by Sherrington, Kirkpatrick and others, was found by Giorgio Parisi in 1979 within the replica method. The subsequent work of interpretation of the Parisi solution by M. Mezard, G. Parisi, M.A. Virasoro and many others, revealed the complex nature of a glassy low temperature phase, characterized by ergodicity breaking, ultrametricity, non-selfaverageness. Further developments led to the creation of the cavity method, allowing to study the low temperature phase without replica. A rigorous proof of the Parisi solution has been provided by the work of Francesco Guerra and Michel Talagrand in the 2000.

Besides its importance in condensed matter physics, spin glass theory has in the time acquired a strongly interdisciplinary character, with applications to neural network theory, computer science, theoretical biology, econophysics etc.

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.

The cavity method has been successfully employed to analyze the typical case of Constraint Satisfaction Problems like the random KSATdn and the coloring of random graphs.

ee also

*Quenched disorder
*Replica trick
*Cavity method
*Geometrical frustration
*Phase transition
*Antiferromagnetic interaction
*Crystal structure
*Spin ice


* K.H. Fischer and J.A. Hertz, "Spin Glasses", Cambridge University Press (1991)
* cite book
last = Mezard
first = Marc
coauthors = Giorgio Parisi, Miguel Angel Virasoro
year = 1987
title = Spin glass theory and beyond
publisher = World Scientific
location = Singapore
id = 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
* [http://xstructure.inr.ac.ru/x-bin/theme2.py?arxiv=cond-mat&level=2&index1=2 Spin glass on arxiv.org]

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • spin glass — noun Any material in which the atomic spins are oriented at disordered but fixed directions …   Wiktionary

  • Spin-Glas — Schematische Darstellung der ungeordneten Struktur eines Spin Glases (top) und eines Ferromagneten (bottom) Ein Spin Glas (auch Spinglas, englisch spin glass) ist ein ungeordnetes magnetisches System mit einer sogenannten geometrischen… …   Deutsch Wikipedia

  • Spin ice — A spin ice is a material where the behavior of the magnetic moments in the material is analogous to the behavior of the protons in water ice. of ice was expected to be non trivial. [L. Pauling, The Structure and Entropy of Ice and of Other… …   Wikipedia

  • Spin coating — is a procedure used to apply uniform thin films to flat substrates. In short, an excess amount of a solution is placed on the substrate, which is then rotated at high speed in order to spread the fluid by centrifugal force. A machine used for… …   Wikipedia

  • Glass — This article is about the material. For other uses, see Glass (disambiguation). Moldavite, a natural glass formed by meteorite impact, from Besednice, Bohemia …   Wikipedia

  • spin — v. & n. v. (spinning; past and past part. spun) 1 intr. & tr. turn or cause (a person or thing) to turn or whirl round quickly. 2 tr. (also absol.) a draw out and twist (wool, cotton, etc.) into threads. b make (yarn) in this way. c make a… …   Useful english dictionary

  • Spin column-based nucleic acid purification — Silica on a minicolumn with water and with DNA sample in chaotropic buffer Column based nucleic acid purification is a solid phase extraction method to quickly purify nucleic acids. This method relies on the fact that the nucleic acid may bind… …   Wikipedia

  • Verre de spin — Représentation schématique d une structure aléatoire d un verre de spins (haut) et d un état ferromagnétique (bas). Les verres de spin sont des alliages métalliques comportant un petit nombre d impuretés magnétiques disposées au hasard dans l… …   Wikipédia en Français

  • The Looking Glass Wars — infobox Book | name = The Looking Glass Wars title orig = translator = image caption = author = Frank Beddor illustrator = cover artist = country = United States language = English series = genre = Fantasy, Novel publisher = Dial release date =… …   Wikipedia

  • The Glass Passenger — Infobox Album Name = The Glass Passenger Type = Studio Artist = Jack s Mannequin Released = USA: September 30, 2008, Aus: October 4, 2008 Recorded = Santa Monica, California Genre = Rock, Piano rock Length = Label = Sire Producer = Andrew McMahon …   Wikipedia