Critical Dynamics of Magnets

We review our current understanding of the critical dynamics of magnets above and below the transition temperature with focus on the effects due to the dipole--dipole interaction present in all real magnets. Significant progress in our understanding of real ferromagnets in the vicinity of the critical point has been made in the last decade through improved experimental techniques and theoretical advances in taking into account realistic spin-spin interactions. We start our review with a discussion of the theoretical results for the critical dynamics based on recent renormalization group, mode coupling and spin wave theories. A detailed comparison is made of the theory with experimental results obtained by different measuring techniques, such as neutron scattering, hyperfine interaction, muon--spin--resonance, electron--spin--resonance, and magnetic relaxation, in various materials. Furthermore we discuss the effects of dipolar interaction on the critical dynamics of three--dimensional isotropic antiferromagnets and uniaxial ferromagnets. Special attention is also paid to a discussion of the consequences of dipolar anisotropies on the existence of magnetic order and the spin--wave spectrum in two--dimensional ferromagnets and antiferromagnets. We close our review with a formulation of critical dynamics in terms of nonlinear Langevin equations.Comment: Review article (154 pages, figures included

Spin alignment of leading K∗(892)0K^{*}(892)^{0} mesons in hadronic Z0Z^0 decays

Helicity density matrix elements for inclusive K*(892)^0 mesons from hadronic Z^0 decays have been measured over the full range of K^*0 momentum using data taken with the OPAL experiment at LEP. A preference for occupation of the helicity zero state is observed at all scaled momentum x_p values above 0.3, with the matrix element rho_00 rising to 0.66 +/- 0.11 for x_p > 0.7. The values of the real part of the off-diagonal element rho_1-1 are negative at large x_p, with a weighted average value of -0.09 +/- 0.03 for x_p > 0.3, in agreement with new theoretical predictions based on Standard Model parameters and coherent fragmentation of the qq(bar) system from the Z^0 decay. All other helicity density matrix elements measured are consistent with zero over the entire x_p range. The K^*0 fragmentation function has also been measured and the total rate determined to be 0.74 +/- 0.02 +/- 0.02 K*(892)^0 mesons per hadronic Z^0 decay.Helicity density matrix elements for inclusive K*(892)^0 mesons from hadronic Z^0 decays have been measured over the full range of K^*0 momentum using data taken with the OPAL experiment at LEP. A preference for occupation of the helicity zero state is observed at all scaled momentum x_p values above 0.3, with the matrix element rho_00 rising to 0.66 +/- 0.11 for x_p > 0.7. The values of the real part of the off-diagonal element rho_1-1 are negative at large x_p, with a weighted average value of -0.09 +/- 0.03 for x_p > 0.3, in agreement with new theoretical predictions based on Standard Model parameters and coherent fragmentation of the qq(bar) system from the Z^0 decay. All other helicity density matrix elements measured are consistent with zero over the entire x_p range. The K^*0 fragmentation function has also been measured and the total rate determined to be 0.74 +/- 0.02 +/- 0.02 K*(892)^0 mesons per hadronic Z^0 decay.Helicity density matrix elements for inclusive K*(892)^0 mesons from hadronic Z^0 decays have been measured over the full range of K^*0 momentum using data taken with the OPAL experiment at LEP. A preference for occupation of the helicity zero state is observed at all scaled momentum x_p values above 0.3, with the matrix element rho_00 rising to 0.66 +/- 0.11 for x_p > 0.7. The values of the real part of the off-diagonal element rho_1-1 are negative at large x_p, with a weighted average value of -0.09 +/- 0.03 for x_p > 0.3, in agreement with new theoretical predictions based on Standard Model parameters and coherent fragmentation of the qq(bar) system from the Z^0 decay. All other helicity density matrix elements measured are consistent with zero over the entire x_p range. The K^*0 fragmentation function has also been measured and the total rate determined to be 0.74 +/- 0.02 +/- 0.02 K*(892)^0 mesons per hadronic Z^0 decay.Helicity density matrix elements for inclusive K*(892)^0 mesons from hadronic Z^0 decays have been measured over the full range of K^*0 momentum using data taken with the OPAL experiment at LEP. A preference for occupation of the helicity zero state is observed at all scaled momentum x_p values above 0.3, with the matrix element rho_00 rising to 0.66 +/- 0.11 for x_p > 0.7. The values of the real part of the off-diagonal element rho_1-1 are negative at large x_p, with a weighted average value of -0.09 +/- 0.03 for x_p > 0.3, in agreement with new theoretical predictions based on Standard Model parameters and coherent fragmentation of the qq(bar) system from the Z^0 decay. All other helicity density matrix elements measured are consistent with zero over the entire x_p range. The K^*0 fragmentation function has also been measured and the total rate determined to be 0.74 +/- 0.02 +/- 0.02 K*(892)^0 mesons per hadronic Z^0 decay.Helicity density matrix elements for inclusive K ∗ (892) 0 mesons from hadronic Z 0 decays have been measured over the full range of K ∗ 0 momentum using data taken with the OPAL experiment at LEP. A preference for occupation of the helicity zero state is observed at all scaled momentum x p values above 0.3, with the matrix element ϱ 00 rising to 0.66 ± 0.11 for x p > 0.7. The values of the real part of the off-diagonal element ϱ 1 - 1 are negative at large x p , with a weighted average value of −0.09 ± 0.03 for x p > 0.3, in agreement with new theoretical predictions based on Standard Model parameters and coherent fragmentation of the q q system from the Z 0 decay. All other helicity density matrix elements measured are consistent with zero over the entire x p range. The K ∗ 0 fragmentation function has also been measured and the total rate determined to be 0.74 ± 0.02 ± 0.02 K ∗ (892) 0 mesons per hadronic Z 0 decay