Her Majesty Symmetry: Symmetry and Order, Phases of Matter, and Phase Transitions
The role of symmetry in the Universe, our life, and in physics is so versatile that one must deal with a particular area. I address the role of symmetry in the physics of macroscopic phases of matter and their transformations called phase transitions. Bodies with very different molecules often represent the same phase of matter because, actually, a macroscopic phase is determined only by its symmetry.Many fundamental effects of phase transition can be predicted considering the symmetry alone, making the calculations involved very simple. Depending on the symmetry of macroscopic phases, the transformation between them, a phase transition, can be of two different kinds. The second order phase transition occurs in bodies with the so-called polar symmetry. This transition is also described as a spontaneous symmetry breaking of the original phase. The common example of polar order is a magnet with molecules bearing magnetic moments (small magnets). The transition from the isotropic (all molecular magnets are oriented chaotically making no macromagnet) to the polar (ferromagnetic) phase occurs when the temperature decreases to the so-called Curie temperature Tc and the energy prevails over entropy. The very important property of this second order transition is that the two phases, the nonmagnetic and magnetic, cannot coexist, i.e., the body is either magnet (below Tc) or non-magnet (above Tc). The first order phase transition occurs in a body with the non-polar symmetry. The common example is a nematic liquid crystal, which has been used as a working optical element in the cell-phone and computer displays. A nematic liquid crystal consists of elongated molecules. When these molecules are oriented chaotically, the liquid is isotropic (dark when seen in a microscope). As the temperature decreases to certain value TNI, the molecules get oriented along single direction called director; such liquid is an anisotropic nematic liquid crystal (colors appear!).The order is non-polar as both directions along the director are indistinguishable. The benchmark of this transition (which is similar to the water-ice transition) is that the two phases, nematic and isotropic (ice and water) can coexist in some narrow temperature interval. The second and first order transitions are very different, but the whole difference is solely in the symmetry of the phase of matter. Thus, the main effects can be predicted without any calculations because only Her Majesty Symmetry rules them.
