Realistic spin glasses below eight dimensions: A highly disordered view

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 63, Issue 1, 2001, Pages

  Newman, C M ^a   Stein, D L ^b  

^a NEW YORK UNIVERSITY   (United States)

^b University of Arizona   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18644370829     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.016101     Document Type: Article

References (43)

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19. A completely rigorous proof, though, has so far been obtained only for (Formula presented).
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32. Below four dimensions, quenched disorder is believed to result in domain wall wandering even at zero temperature. Domain wall wandering occurs also in uniform ferromagnets above the roughening temperature (which is zero in two dimensions and believed to be strictly below (Formula presented) in three dimensions), but for a different reason—resulting from thermal fluctuations, rather than from quenched disorder.
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43. The possibility that dimension eight plays a special role in short-ranged spin glasses has been suggested previously, but for different reasons; see D. S. Fisher and H. Sompolinsky, Phys. Rev. Lett. 54, 1063 (1985). However, we emphasize that our claim is not that dimension eight necessarily plays a special role—only that the most likely conclusion of our analysis, of a single pair of low-temperature pure states, holds at least up to eight dimensions.