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G. (π, 0) and (2π, π), the spin waves should also be dispersionless along the magnetic 34 Strong interactions in low dimensions zone boundary as well. However, when quantum corrections are inserted, this degeneracy is lifted. This follows because the classical N´eel state is not the actual ground state for the system, and the real ground state wavefunction contains corrections involving spins flipped relative to simple unit cell doubling. If a spin displaced along the diagonal from such a defect is flipped to build the wavefunction for a spin wave, the energy cost remains 4J, as for the undisturbed N´eel state.
Indeed, this is the only case we are aware of where two of the quantum critical exponents expected for a two-dimensional antiferromagnet have actually been observed. To give more detail, we refer to the schematic phase diagram[101], shown in Fig. 23, for the cuprates. Here, the variables are doping x, chemical pressure y, and temperature, T . There are several phases, including the parent antiferromagnet (AFM), the high temperature superconductor (SC), spin glass (SG), and a longer period antiferromagnet commonly referred to as ’striped’.
Broholm, S. Lance Cooper, J. E. Crow, P. C. Hammel, G. Lander, Physica B 318, 12-23 (2002). M. Lovesey, Theory of Thermal Neutron Scattering from Condensed Matter, (Clarendon Press, Oxford) 1984. REFERENCES 57 [5] P. J. Brown, in “International Tables for Crystallography”, Volume C, edited by A. J. C. Prince, Kluwer Academic Publishers Boston (1999). [6] J. M. Tranquada, G. Shirane, S. M. Shapiro, ”Neutron Scattering with a Triple-Axis Spectrometer”, Cambridge University Press (2002). [7] K. Skj¨ old and D.