Griffiths effects in random Heisenberg antiferromagnetic S = 1 chains

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 10, 2002, Pages 1044251-10442516

  Damle, Kedar ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ACCELERATION; ARTICLE; CALCULATION; DENSITY; DIMERIZATION; ENERGY; HEAT; LOW TEMPERATURE; MAGNETISM; MATHEMATICAL ANALYSIS; PHASE SEPARATION;

EID: 0036752844     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

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16. Note that our effective model bears some resemblance to the model proposed in Ref. 16 to analyze the effects of randomness on antiferromagnetic S = 3/2 chains, although the physics is quite different.
17. S.K. Ma, C. Dasgupta, and C.K. Hu, Phys. Rev. Lett. 43, 1434 (1979); for a more detailed discussion, also see C. Dasgupta and S.K. Ma, Phys. Rev. B 22, 1305 (1980).
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19. F. Igloi, cond-mat/0108350 (unpublished).
20. a = 1,q = 0). I use the slightly more general formulation given here since it corresponds to the physical picture developed in the earlier section.
21. K. Damle and D.A. Huse, cond-mat/0207244 (unpublished).
22. RS, quoted in a footnote of Ref. 6 instead of the value derived earlier in Ref. 13; see also Ref. 22 below for a 'percolation' picture reducing this to Fisher's original result (Ref. 23) for the corresponding magnetization exponent of the random transverse field Ising chain.
23. w constitutes a special case-at any point along this line, there is, in addition to two marginal perturbations, a marginally relevant perturbation (growing as a power of Γ), which simply reflects the fact that any point in the (1,1) phase with δ > 0 has q = 0, reflecting the extreme paucity of s-type even bonds relative to the w-type even bonds at low enough energies, while, precisely at δ = 0, there is no such distinction between the s-type and w-type even bonds, and q = 1/2.
24. a is driven to either 1 or 0 as soon as one moves off the cross-over line, while at any point along this line, it takes some non-universal value between these two extremes.
25. O. Motrunich, K. Damle, and D.A. Huse, Phys. Rev. B 63, 224204 (2001).
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27. 1 line exists only for r > 0.
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29. K. Damle, O. Motrunich, and D.A. Huse, Phys. Rev. Lett. 84, 3434 (2000); also see O. Motrunich, K. Damle, and D.A. Huse, Phys. Rev. B 63, 134424 (2001).
30. G. Refael, S. Kehrein, and D.S. Fisher, Phys. Rev. B 66, 060402 (2002).
31. K. Damle, D. A. Huse, and G. Refael, (unpublished).