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Articles: Devotion | In quest of infinity - 9
- Prof. venkata ramanamurty mallajosyula
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The concept of order-disorder in magnetic solids. In both (a) and (b), we have a schematic depiction of [crystalline] iron via an array of arrows arranged on a [2D] lattice. The arrows here are symbolic of the fact that every iron atom is a tiny magnet. The way the arrow points is representative of the way the elementary magnets point [see inset in (a)].
The difference between the two figures is in the way the arrows point on the whole. In (a), the arrows point randomly, representing magnetic disorder, the state that prevails above 770°C. In (b), the arrows all point in one common direction, indicative of magnetic order [the state that prevails below 770°C. The critical temperature, namely 770°C, marks the order-disorder transition temperature for iron.
The change from a state when the atomic magnetic point randomly to the state when they all point in the same direction is called a phase transition. When the tiny magnets point randomly, obviously there is no magnetic order but when they all point in the same direction, there is magnetic order. In the state when there is no magnetic order, the order parameter has a value equal to zero, while when magnetic order is established, the order parameter assumes a non-zero value. So we have this rule: High temperature state, no order, and order parameter equals zero; low temperature state, there is order, and order parameter has a value that is non-zero.
OK, all this is fine but where do symmetry and symmetry-breaking come into all this? That is what I shall now briefly describe. Just take a look at the figures below.
To illustrate the important idea of symmetry-breaking. Case (a) deals with the disordered state of iron while case (b) deals with the ordered state. Consider first (a). Imagine that the arrow in every lattice site is rotated by the same angle. We describe this by saying that a rotation is performed on the magnetic system. The illustration in (a-i) represents the situation before rotation and that in (a-ii) represents the situation after rotation. When the number of arrows is small, we could of course distinguish the two patterns, but when the number of arrows is large, it is difficult to distinguish the two.
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