Quantum critical behavior of clean itinerant ferromagnets

Zeitschrift fur Physik B-Condensed Matter

Volumn 103, Issue 3, 1997, Pages 451-461

  Vojta, Thomas ^a,b   Belitz, D ^a   Narayanan, R ^a   Kirkpatrick, T R ^c  

^a UNIVERSITY OF OREGON   (United States)

^b CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

^c Bldg 142   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001446689     PISSN: 07223277     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002570050399     Document Type: Article

References (25)

1. J. A. Hertz, Phys. Rev. B 14, 1165 (1976). For earlier thoughts about quantum phase transitions, see the references therein
2. We use the term 'LGW theory' in the narrow sense, in which it is usually used in the literature, of an effective field theory in terms of the order parameter field only. If one defines it as an effective theory for all soft modes, then it is valid in the present case, too
3. S. Sachdev, Z. Phys. B 94, 469 (1994)
4. D. Belitz and T.R. Kirkpatrick, Europhys. Lett. 35, 201 (1996);
5. T. R. Kirkpatrick and D. Belitz, Phys. Rev. B 53, 14364 (1996)
6. T. Vojta, D. Belitz, R. Narayanan, and T. R. Kirkpatrick, Europhys. Lett. 36, 191 (1996) (cond-mat/9510146)
7. See, e.g., J.W. Negele and H. Orland, Quantum Many-Particle Systems. Addison Wesley (New York 1988)
8. See, e.g., A. A. Abrikosov, L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics. New York: Dover 1975
9. This becomes clearer in Fourier space, where the sums over wavenumbers that replace the real space integrals in (2.5a) extend over small wavenumbers only. See, e.g., [12] for a more detailed exposition of this point
10. c are the zero angular momentum (l = 0) components in a multipole expansion of the respective interaction potentials, and hence are related to the l = 0 Landau parameters. The physics we are interested in is due to hydrodynamic effects, which are strongest in the l = 0 or density channel. This justifies our neglecting the higher Fermi liquid parameters
11. See, e.g., K. G. Wilson and J. Kogut, Phys. Rep. 12, 75 (1974)
12. Fq
13. D. Belitz, T. R. Kirkpatrick, and T. Vojta, cond-mat/9611099, to appear in Phys. Rev. B
14. d-1 > 0, since else the continuous ferromagnetic phase transition we are interested in does not exist
15. 0(9 = 0) as a function of temperature in d = 3 does not show a corresponding nonanalyticity. This does not contradict the nonanalytic q-dependence at zero temperature, see [12]
16. T. R. Kirkpatrick and D. Belitz, cond-mat/9602144, to appear in J. Stat. Phys
17. M. E. Fisher, in: Advanced Course on Critical Phenomena. F. W. Hahne (ed.) New York: Springer 1983
18. A. J. Millis, Phys. Rev. B 48, 7183 (1993)
19. S. Sachdev, Phys. Rev. B 55, 142 (1997)
20. For all dimensions d > 2, where there is a classical Heisenberg transition, there is still another crossover in the system, namely from the classical Gaussian region to the classical Heisenberg critical region. For 1 < d < 2, where there is no long-range order at any nonzero temperature, this is not the case. In either case, φ describes the leading low-temperature effect due to the relevance of the temperature with respect to the quantum fixed point
21. D. Belitz and T. R. Kirkpatrick, J. Phys. Cond. Matt. 8, 1 (1996)
22. See, e.g., S. K. Ma, Modern Theory of Critical Phenomena. Reading, MA: Benjamin 1976
23. F. J. Wegner, in Phase Transitions and Critical Phenomena, vol.6, C. Domb and M. S. Green (eds.) New York: Academic Press 1976
24. t, which in the present language also involves some two-loop diagrams
25. M. E. Fisher, S.-K. Ma, and B. G. Nickel, Phys. Rev. Lett. 29, 917 (1972)