Spin glass

A spin- glass (including spin-glass, spin- glass English ) is a spin with respect to its structure and position of the magnetic system with a disordered spin disordered so-called geometric frustration. This is a quantifiable measure of the inability of the system to achieve a simple spin state of lowest energy ( ground state) and can be mathematically precise manner without using the energy concept. Spin- glasses (but also certain conventionally - level systems ) have extremely large number of metastable states, which never can all be run on experimentally accessible time scales. Typical cause of frustration is in spin- glasses the simultaneous presence of

The phenomenon of " frustration " in the sense described above occurs, for example, if an odd number of spins antiferromagnetically interact. The term was adopted by exploiting cross- relationships in a modified form by the Frenchman Gérard Toulouse from high-energy physics (see quantum chromodynamics and Wilson loop, after the American Nobel Laureate Kenneth Wilson).

Compared with other magnetic systems

Brings to a spin- glass to a (low ) external magnetic field, and records the magnetization as a function of temperature, as is observed above the transition temperature Tf of a "typical" magnetically - chaotic behavior (such as in paramagnetism, but other types of magnetism are possible). The magnetization follows the Curie law, according to which the magnetization is inversely proportional to temperature. Falls below the critical temperature, the temperature Tf, can be reached as the spin-glass phase, and the magnetization is practically constant. Its value is referred to as "field cooled". The external magnetic field is switched off, the magnetization of the spin- glass is initially obtained quickly from the remanent magnetization, and then slowly approaches zero (or a small fraction of the initial magnetization, it is not yet known). This decrease is not exponential and is characterized spin glasses. Experimental measurements have shown continuous changes in the magnetization above the noise limit of the measuring devices in the order of days.

In contrast to the spin glass falls in a ferromagnetic material, the magnetization after switching off the external field to a specific value ( residual magnetization ), which remains constant in the other time. At a paramagnet the magnetization falls with switching off the external field, rapidly decreases to zero. In both cases the waste is carried out exponentially with a very small time constant.

If you cool a spin- glass without external field below the transition temperature, and brings it afterwards in a magnetic field, the magnetization rises rapidly to the so-called " zero-field -cooled magnetization ", which is lower than the above mentioned " field -cooled magnetization ," and then approaches slowly to the field -cooled value.

Theory

In the theory of spin glasses to be widely used simplified models, but are intended to describe the essentials (ie, a distinction is relevant and irrelevant properties). For example, it describes the so-called Edwards -Anderson model, the spin glass by a spin model with Ising degrees of freedom and from place to place randomly distributed interaction constants as random distribution to use this Gaussian distributions, and only nearest-neighbor interactions are taken into account. Are you on the latter restriction, we obtain the strong examined Sherrington - Kirkpatrick model ( according to David Sherrington and Scott Kirkpatrick 1975). Even easier is the ± 1 spin glass in which it is assumed that one has to deal only with binary spin degrees of freedom of the species, with positive and negative interactions with a matching amount equal often.

Importance of the theory of spin glasses

Spin glasses are therefore not only investigated experimentally, but also extensively theoretically and simulated on the computer using numerical methods. A large portion of the early work on theoretical spin glass uses a form of the mean-field theory, based on a set of so-called replicas of the state function of the system. An important, simple way apparently (!) Exactly solvable model of a spin glass was, as mentioned, introduced by Sherrington and Kirkpatrick and led to significant extensions of the mean-field theory to describe the slow dynamics of the magnetization and of the complex non - ergodic equilibrium state. Instead of the specified Sherrington and Kirkpatrick simple and seemingly exact solution of their model became one derived from Giorgio Parisi complicated result, with an order parameter function q ( x ) instead of the usual simple order parameter q. Parisi found in this context, a special hierarchical method for " replica symmetry breaking ", which has been found on the spin-glass theory also in other contexts application ( see below).

The non- ergodic behavior of the system below the freezing temperature Tf is that the system " hangs " at these temperatures in the deep valleys of the resulting hierarchical- disordered energy landscape.

Applications

Although spin-glass magnetism typically only below a temperature of about 30 Kelvin ( -240 degrees Celsius ≈ ) occurs and thus appears in practice to be totally useless, he has in other contexts, eg in the theory of so-called neuronal networks, that is, in the theoretical brain research, application found. The same is true for the mathematical- economics optimization theory.