Excerpt

By the early 1970s, physicists had synthesized a comprehensive mathematical and conceptual framework for understanding microscopic and bulk properties of “organized matter” (now commonly referred to as condensed matter). Condensed-matter systems are assemblies of a vast number (typically of order 10^24–10^25) of interacting atoms or molecules, and they include materials as diverse as crystalline solids, magnetic systems, superconductors, and liquid crystals, among many others. All share the property of emergence: the collective behavior of the system as a whole cannot be readily predicted or understood by our knowledge, no matter how complete, of the individual isolated constituents.

This synthesis, which underlies the modern field of condensed-matter physics, rests on three foundations. Two of these, quantum mechanics and thermodynamics (including statistical mechanics), are well-established subjects taught in all modern-day undergraduate physics curricula. The third—symmetry—is less well-known but has played a central role in our modern understanding of the physical universe. For our purposes, it will be sufficient to note that many of the emergent behaviors of condensed-matter systems—the solidity of lead, the magnetic behavior of iron, the superconductivity of mercury—are intimately related to a change in the organizational symmetry of their microscopic constituents at a phase transition, such as that from water to ice. Each molecule in liquid water is free to travel anywhere within the liquid, and the positions of its molecules at any moment appear random; in contrast, each molecule in solid ice is confined to a very small region of space, and the overall organization of molecules in ice forms a regular, repeating structure called a crystalline lattice.

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