Nonanalytic magnetization dependence of the magnon effective mass in itinerant quantum ferromagnets

Physical Review B - Condensed Matter and Materials Physics

Volumn 58, Issue 21, 1998, Pages 14155-14158

  Belitz, D ^a   Kirkpatrick, T ^a   Millis, A ^a   Vojta, Thomas ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000391348     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.58.14155     Document Type: Article

References (12)

1. See, e.g., D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (Benjamin, Reading, MA, 1975).
2. T. Moriya, Spin Fluctuations in Itinerant Electron Magnetism (Springer, Berlin 1985).
3. T. R. Kirkpatrick and D. Belitz, Phys. Rev. B 53, 14 364 (1996).
4. T. Vojta, D. Belitz, R. Narayanan, and T. R. Kirkpatrick, Z. Phys. B 103, 451 (1996).
5. For a review, see, e.g., P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985).
6. See, e.g., G. Baym and C. Pethick, Landau Fermi-Liquid Theory (Wiley, New York, 1991).
7. D. Belitz and T. R. Kirkpatrick, Phys. Rev. B 56, 6513 (1997).
8. D. Belitz, T. R. Kirkpatrick, and T. Vojta, Phys. Rev. B 55, 9452 (1997).
9. J. A. Hertz, Phys. Rev. B 14, 1165 (1976).
10. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Clarendon, Oxford, 1989).
11. It is important that even the longitudinal spin susceptibility of electrons in a magnetic field shows no nonanalytic wave-number dependence of the type found in zero magnetic field, even though the soft-mode structure would in principle allow for one; see D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66, 261 (1994), Sec. V A 2 for the disordered case, and T. Vojta (unpublished) for the clean one. The cancellations governed by these Ward identities reflect the fact that the vertices of the exact effective (Formula presented)-field theory are still transverse correlation functions in some (complicated) reference system. Rotational invariance of the spins in this reference ensemble then ensures the softness of the transverse modes in the same way as it is ensured in the simple reference system (Formula presented) that corresponds to our saddle-point approximation for the (Formula presented) fluctuations.
12. For a review, see D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66, 261 (1994).