By Philip W. Anderson

Uncomplicated Notions of Condensed subject Physics is a transparent creation to a couple of the main major innovations within the physics of condensed topic. the final ideas of many-body physics and perturbation conception are emphasized, offering supportive mathematical constitution. this is often a selection and restatement of the second one half Nobel Laureate Philip Anderson’s vintage strategies in Solids.

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BROKEN SYMMETRY E. GENERALIZED RIGIDITY AND LONG-RANGE ORDER: THEORY 49 MEASUREMENT We are so accustomed to the rigidity of solid bodies-the idea, for instance, that when we move one end of a ruler, the other end moves the same distance--that it is hard to realize that such action at a distance is not built into the laws of nature except in the case of the long-range forces such as gravity or electrostatics. It is strictly a consequence of the fact that the energy is minimized when symmetry is broken in the same way throughout the sample: the phase and angle variables want to be uniform, so that the orientation and position of the lattice is the same everywhere.

By using ~L. ' {r} This is Bloch's way of producing spin waves; but it is just a linear combination of the classical Herring-Kittel way of producing a spin wave (Herring and Kittel, 1951), which is to allow a small spiral precession of the quantization axis of the total spin. Bloch showed that the resulting state is to an excellent approximation an eigenstate; we shall give a semiclassical derivation of this same result below. e, the effective Hamiltonian must always be« (VS)2. Therefore a slow twist of S must be a very low energy excitation.

20) This question is related to that of the "dimensionality of the order parameter," which plays a great role in critical fluctuation theory. " An example is the Ising model for ferromagnetism, which is isomorphic symmetrywise, with the ferromagnet with axial anisotropy having the favored direction along the axis. In the Ising model, there is no question of collective modes, because there are no continuous degrees of freedom to support them, whereas in the axial ferromagnet, the modes are there but do not appear at zero frequency; they have a frequency proportional to the anisotropy.