Abstract
The statistics of domain walls for ground states of the 2D Ising spin glass with +1 and −1 bonds are studied for L × L square lattices with L ≤ 48, and p = 0.5, where p is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. When L is even, almost all domain walls have energy E dw = 0 or 4. When L is odd, most domain walls have E dw = 2. The probability distribution of the entropy, S dw , is found to depend strongly on E dw . When E dw = 0, the probability distribution of |S dw | is approximately exponential. The variance of this distribution is proportional to L, in agreement with the results of Saul and Kardar. For E dw = k > 0 the distribution of S dw is not symmetric about zero. In these cases the variance still appears to be linear in L, but the average of S dw grows faster than L. This suggests a one-parameter scaling form for the L-dependence of the distributions of S dw for k> 0.
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References
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35:1972 (1975).
G. Parisi, J. Phys. A 13:1101, 1887 and L115 (1980).
G. Parisi, Phys. Rev. Lett. 50:1946 (1983).
D. S. Fisher and D. A. Huse, Phys. Rev. Lett. 56:1601 (1986).
D. A. Huse and D. S. Fisher, Phys. Rev. Lett. 57:2203 (1986).
D. S. Fisher and D. A. Huse, Phys. Rev. B 38:386 (1988).
W. L. McMillan, J. Phys. C 17:3179 (1984).
W. L. McMillan, Phys. Rev. B 29:4026 (1984).
W. L. McMillan, Phys. Rev. B 31:340 (1985).
A. J. Bray and M. A. Moore, Phys. Rev. B 31:631 (1985).
A. J. Bray and M. A. Moore, Heidelberg Colloquium on Glassy Dynamics, J. L. van Hemmen and I. Morgenstern, Ed., (Springer, Berlin, 1986), pp. 121–153.
A. J. Bray and M. A. Moore, Phys. Rev. Lett. 58:57 (1987).
C. Amoruso, E. Marinari, O. C. Martin and A. Pagnani, Phys. Rev. Lett. 91:087201 (2003).
C. Amoruso, A. K. Hartmann, M. B. Hastings and M. A. Moore, cond-mat/0601711.
H. G. Katzgraber and L. W. Lee, Phys. Rev. B 71:134404 (2005).
J Poulter and J. A. Blackman, Phys. Rev. B 72:104422 (2005).
A. K. Hartmann and A. P. Young, Phys. Rev. B 64:180404(R) (2001).
L. Saul and M. Kardar, Phys. Rev. E 48:R3221 (1993).
L. Saul and M. Kardar, Nucl. Phys. B 432:641 (1994).
R. Fisch, J. Stat. Phys., to appear (2006), cond-mat/0502605.
R. Fisch, cond-mat/0508468.
C. Wang, J. Harrington and J. Preskill, Ann. Phys. (N.Y.) 303:31 (2003).
A. Galluccio, M. Loebl and J. Vondrák, Phys. Rev. Lett. 84:5924 (2000).
J. W. Landry and S. N. Coppersmith, Phys. Rev. B 65:134404 (2001).
S. F. Edwards and P. W. Anderson, J. Phys. F 5:965 (1975).
This issue was ignored by Saul and Kardar.
I. A. Campbell, A. K. Hartmann and H. G. Katzgraber, Phys. Rev. B 70:054429 (2004).
A. K. Hartmann, A. J. Bray, A. C. Carter, M. A. Moore and A. P. Young, Phys. Rev. B 66:224401 (2002).
R. Fisch and A. K. Hartmann, cond-mat/0603729.
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PACS: 75.10.Nr, 75.40.Mg, 75.60.Ch, 05.50.+q
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Fisch, R. Finite-Size Scaling of the Domain Wall Entropy Distributions for the 2D ± J Ising Spin Glass. J Stat Phys 125, 793–803 (2006). https://doi.org/10.1007/s10955-006-9223-7
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DOI: https://doi.org/10.1007/s10955-006-9223-7