Spin Glass
A Spin Glass is a disordered magnet where the magnetic spin of the component atoms (the orientation of the north and south magnetic poles in three-dimensional space) are not aligned in a regular pattern.
- Example(s):
- See: Artificial Neural Networks, Magnet, Glass, Amorphous, Crystal, Ferromagnetic, Antiferromagnet, Geometrical Frustration, Metastable, Simulation.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Spin_glass Retrieved:2015-2-28.
- A spin glass is a disordered magnet, where the magnetic spin of the component atoms (the orientation of the north and south magnetic poles in three-dimensional space) are not aligned in a regular pattern. 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. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solid, magnetic spins all align in the same direction; this would be analogous to a crystal.
The individual atomic bonds in a spin glass are a mixture of roughly equal numbers of ferromagnetic bonds (where neighbors have the same orientation) and antiferromagnetic bonds (where neighbors have exactly the opposite orientation: north and south poles are flipped 180 degrees). These patterns of aligned and misaligned atomic magnets create what are known as frustrated interactions - distortions in the geometry of atomic bonds compared to what would be seen in a regular, fully aligned solid. They may also create situations where more than one geometric arrangement of atoms is stable.
Spin glasses and the complex internal structures that arise within them are termed “metastable” because they are "stuck" in stable configurations other than the lowest-energy configuration (which would be aligned and ferromagnetic). The mathematical complexity of these structures are difficult but fruitful to study experimentally or in simulations, with applications to artificial neural networks in computer science in addition to physics, chemistry, and materials science.
- A spin glass is a disordered magnet, where the magnetic spin of the component atoms (the orientation of the north and south magnetic poles in three-dimensional space) are not aligned in a regular pattern. 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. In window glass or any amorphous solid the atomic bond structure is highly irregular; in contrast, a crystal has a uniform pattern of atomic bonds. In ferromagnetic solid, magnetic spins all align in the same direction; this would be analogous to a crystal.
1982
- Barahona, Francisco. "On the computational complexity of Ising spin glass models.” In: Journal of Physics A: Mathematical and General 15, no. 10 (1982): 3241.
- ABSTRACT: In a spin glass with Ising spins, the problems of computing the magnetic partition function and finding a ground state are studied. In a finite two-dimensional lattice these problems can be solved by algorithms that require a number of steps bounded by a polynomial function of the size of the lattice. In contrast to this fact, the same problems are shown to belong to the class of NP-hard problems, both in the two-dimensional case within a magnetic field, and in the three-dimensional case. NP-hardness of a problem suggests that it is very unlikely that a polynomial algorithm could exist to solve it.