Papers
Topics
Authors
Recent
Search
2000 character limit reached

Universal fragility of spin-glass ground-states under single bond changes

Published 17 May 2023 in cond-mat.dis-nn and cond-mat.stat-mech | (2305.10376v3)

Abstract: We consider the effect of perturbing a single bond on ground-states of nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the coupling constants, across various two and three-dimensional lattices and regular random graphs. Our results reveal that the ground-states are strikingly susceptible to such changes. Altering the strength of only a single bond beyond a critical threshold value leads to a new ground-state that differs from the original one by a droplet of flipped spins whose boundary and volume diverge with the system size -- an effect that is reminiscent of the more familiar phenomenon of disorder chaos. These elementary fractal-boundary zero-energy droplets and their composites feature robust characteristics and provide the lowest-energy macroscopic spin-glass excitations. Remarkably, within numerical accuracy, the size of such droplets conforms to a nearly universal power-law distribution with exponents dependent on the spatial dimension of the system. Furthermore, the critical coupling strengths adhere to a stretched Gaussian distribution that is predominantly determined by the local coordination number.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (53)
  1. M. Mezard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond (Singapore: World Scientific, 1987).
  2. D. L. Stein and C. M. Newman, Spin Glasses and Complexity (Princeton University Press, 2013).
  3. F. Menczer, S. Fortunato, and C. A. Davis, A First Course in Network Science (Cambridge University Press, 2020).
  4. M. Newman, Networks: An Introduction (second Edition) (Oxford University Press, 2018).
  5. J. D. Bryngelson and P. G. Wolynes, Spin glasses and the statistical mechanics of protein folding, Proc. Natl. Acad. Sci. U.S.A. 84, 7425 (1987).
  6. D. Sherrington and S. Kirkpatrick, Solvable model of a spin-glass, Phys. Rev. Lett. 35, 1792 (1975).
  7. B. Derrida, Random-energy model: Limit of a family of disordered systems, Phys. Rev. Lett. 45, 79 (1980).
  8. B. Derrida, Random-energy model: An exactly solvable model of disordered systems, Phys. Rev. B 24, 2613 (1981).
  9. D. J. Gross and M. Mezard, The simplest spin-glass, Nucl. Phys. B 240, 431 (1984).
  10. S. Edwards and P. W. Anderson, Theory of spin glasses, J. Phys. F 5, 965 (1975).
  11. A delicate interplay exists between the latter two (continuum coupling and thermodynamic system size) limits. These two limits do not commute with one another [13].
  12. Degeneracies arise for special values of the coupling constants (a set of measure zero).
  13. M. Palassini and S. Caracciolo, Universal finite-size scaling functions in the 3D Ising spin glass, Phys. Rev. Lett. 82, 5128 (1999).
  14. H. G. Katzgraber, M. Körner, and A. P. Young, Universality in three-dimensional Ising spin glasses: A Monte Carlo study, Phys. Rev. B 73, 224432 (2006).
  15. M. Hasenbusch, A. Pelissetto, and E. Vicari, The critical behavior of 3D Ising glass models: universality and scaling corrections, J. Stat. Mech.: Theory and Exp. 2008, L02001 (2008).
  16. S. Boettcher, Stiffness of the Edwards-Anderson model in all dimensions, Phys. Rev. Lett. 95, 197205 (2006).
  17. G. Parisi and T. Temesvári, Replica symmetry breaking in and around six dimensions, Nuclear Physics B 858, 293 (2012).
  18. W. L. McMillan, Scaling theory of Ising spin glasses, J. Phys. C 17, 3179 (1984).
  19. D. S. Fisher and D. A. Huse, Equilibrium behavior of the spin-glass ordered phase, Phys. Rev. B 38, 386 (1988).
  20. A. J. Bray and M. A. Moore, Scaling theory of the ordered phase of spin glasses, in Heidelberg Colloquium on Glassy Dynamics, edited by J. L. van Hemmen and I. Morgenstern (Springer, Heidelberg, 1987) p. 121.
  21. F. Krzakala and O. C. Martin, Spin and link overlaps in three-dimensional spin glasses, Phys. Rev. Lett. 85, 3013 (2000).
  22. M. Palassini and A. P. Young, Nature of the Spin Glass State, Phys. Rev. Lett. 85, 3017 (2000).
  23. F. Houdayer, J. Krzakala and O. C. Martin, Large-scale low-energy excitations in 3-d spin glasses, Eur. Phys. J. B 18, 467 (2000).
  24. C. M. Newman and D. L. Stein, Metastate approach to thermodynamic chaos, Phys. Rev. E 55, 5194 (1997).
  25. C. M. Newman and D. L. Stein, Ground State Stability and the Nature of the Spin Glass Phase, Phys. Rev. E 105, 044132 (2022).
  26. M. Cieplak and J. R. Banavar, Sensitivity to boundary conditions of Ising spin-glasses, Phys. Rev. B 27, 293 (1983).
  27. A. J. Bray and M. A. Moore, Lower critical dimension of Ising spin glasses: a numerical study, J. Phys. C 17, L463 (1984).
  28. A. K. Hartmann and A. P. Young, Lower critical dimension of Ising spin glasses, Phys. Rev. B 64, 180404 (2001).
  29. A. K. Hartmann and M. A. Moore, Generating droplets in two-dimensional Ising spin glasses using matching algorithms, Phys. Rev. B 69, 104409 (2004).
  30. V. Mohanty and A. A. Louis, Robustness and stability of spin-glass ground states to perturbed interactions, Phys. Rev. E 107, 014126 (2023).
  31. E. Marinari and G. Parisi, Effects of a bulk perturbation on the ground state of 3d ising spin glasses, Phys. Rev. Lett. 86, 3887 (2001).
  32. C. Newman and D. Stein, Nature of ground state incongruence in two-dimensional spin glasses, Phys. Rev. Lett. 84, 3966 (2000).
  33. Here, σksubscript𝜎𝑘\sigma_{k}italic_σ start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT denotes the current spin at site k𝑘kitalic_k following the spin inversion. The prefactor of two is a consequence of the sign inversion of the initial σi⁢σjsubscript𝜎𝑖subscript𝜎𝑗\sigma_{i}\sigma_{j}italic_σ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_σ start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT following the spin flip in D𝐷Ditalic_D.
  34. See Supplemental Material:.
  35. L.-P. Arguin, C. M. Newman, and D. L. Stein, A relation between disorder chaos and incongruent states in spin glasses on Zdsuperscript𝑍𝑑{Z}^{d}italic_Z start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT, Commun. Math. Phys. 367, 1019 (2019).
  36. C. K. Thomas and A. A. Middleton, Matching Kasteleyn cities for spin glass ground states, Phys. Rev. B. 76, 220406 (2007).
  37. V. Kolmogorov, Blossom V: a new implementation of a minimum cost perfect matching algorithm, Math. Program. Comput. 1, 43 (2009).
  38. Gurobi Optimization, LLC, Gurobi Optimizer Reference Manual (2022).
  39. https://github.com/renesmt/ZED.
  40. This follows from Eq. (2) and property (ii).
  41. We further monitor boundary effects and the cutoff 𝒜0subscript𝒜0\mathcal{A}_{\mathrm{0}}caligraphic_A start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT when using open boundary conditions; on a square lattice, ZED perimeters of odd integer lengths are possible only for 𝒜>𝒜0𝒜subscript𝒜0\mathcal{A}>\mathcal{A}_{\mathrm{0}}caligraphic_A > caligraphic_A start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT (when ZEDs touch the boundary).
  42. H. Khoshbakht and M. Weigel, Domain-wall excitations in the two-dimensional Ising spin glass, Phys. Rev. B 97, 064410 (2018).
  43. A. J. Bray and M. A. Moore, Chaotic nature of the spin-glass phase, Phys. Rev. Lett. 58, 57 (1987b).
  44. A. A. Middleton, Energetics and geometry of excitations in random systems, Phys. Rev. E 63, 060202(R) (2001).
  45. F. Krzakala and J.-P. Bouchaud, Disorder chaos in spin glasses, EPL 72, 472 (2005).
  46. H. G. Katzgraber and F. Krzakala, Temperature and Disorder Chaos in Three-Dimensional Ising Spin Glasses, Phys. Rev. Lett. 98, 017201 (2007).
  47. D. Hu, P. Ronhovde, and Z. Nussinov, Phase transitions in random Potts systems and the community detection problem: spin-glass type and dynamic perspectives, Philos. Mag. 92, 406 (2012).
  48. W. Wang, J. Machta, and H. G. Katzgraber, Chaos in spin glasses revealed through thermal boundary conditions, Phys. Rev. B 92, 094410 (2015).
  49. W.-K. Chen and A. Sen, Parisi formula, disorder chaos and fluctuation for the ground state energy in the spherical mixed p-spin models, Comm. Math. Phys. 350, 129 (2017).
  50. O. Melchert, autoscale.py - a program for automatic finite-size scaling analyses: A user’s guide (2009), arXiv:0910.5403 [physics.comp-ph] .
  51. J. Houdayer and A. K. Hartmann, Low-temperature behavior of two-dimensional gaussian ising spin glasses, Phys. Rev. B 70, 014418 (2004).
  52. L. Münster and M. Weigel, Cluster percolation in the two-dimensional Ising spin glass, Phy. Rev. E 107, 054103 (2023).
  53. G. Parisi, Infinite Number of Order Parameters for Spin-Glasses, Phys. Rev. Lett. 43, 1754 (1979).
Citations (2)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Paper to Video (Beta)

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up