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Volumn 63, Issue 22, 2001, Pages

Ising models of quantum frustration

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

EID: 0034896225     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.63.224401     Document Type: Article
Times cited : (465)

References (76)
  • 3
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    • In truth, the issue is somewhat delicate in this particular case with the zero-temperature limit of the spin correlations being critical (Ref. 4). A better example is the kagomé-lattice Ising antiferromagnet (Fig. 22); we will return to these subtleties below
    • In truth, the issue is somewhat delicate in this particular case with the zero-temperature limit of the spin correlations being critical (Ref. 4). A better example is the kagomé-lattice Ising antiferromagnet (Fig. 22); we will return to these subtleties below.
  • 7
    • 85038323467 scopus 로고    scopus 로고
    • cond-mat/0010301, Can. J. Phys. (to be published)
    • For a review, see R. Moessner, cond-mat/0010301, Can. J. Phys. (to be published).
    • Moessner, R.1
  • 8
    • 85038321976 scopus 로고    scopus 로고
    • cond-mat/9708171 (unpublished)] appears to be an example of an ordered system with extensive entropy at (Formula presented) as is a three-leg ladder that we discuss below
    • We should note that there is considerable laxity in the literature regarding the meaning of the term “frustrated magnet” even for classical systems. It would be best to restrict it to systems that have an extensive entropy or ground-state dimensionality at (Formula presented) but it is not unusual to use it to describe all systems with bond interactions that are not simultaneously satisfiable. An instance of the latter, but not of the former is the triangular-lattice Heisenberg model. We should also note that even with the more restricted usage it is not synonymous with absence of ordering—a constrained four-states Potts model on the square lattice [J. K. Burton and C. L. Henley, cond-mat/9708171 (unpublished)] appears to be an example of an ordered system with extensive entropy at (Formula presented) as is a three-leg ladder that we discuss below.
    • Burton, J.K.1    Henley, C.L.2
  • 11
    • 0001349396 scopus 로고
    • Zh. Eksp. Teor. Fiz. 83, 326 (1982)
    • E. F. Shender, Zh. Eksp. Teor. Fiz. 83, 326 (1982) [Sov. Phys. JETP 56, 178 (1982)].
    • (1982) Sov. Phys. JETP , vol.56 , pp. 178
    • Shender, E.F.1
  • 16
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    • F. Mila, Phys. Rev. Lett. 81, 2356 (1998), and references therein.
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 2356
    • Mila, F.1
  • 19
    • 85038339042 scopus 로고    scopus 로고
    • In the future we hope to explore other instances of single-spin quantum dynamics involving either larger values of spin or the extension of classical continuous-spin models to quantum-rotor models. The quantum dynamics of mobile holes in a frustrated Ising background is discussed in Ref. 15
    • In the future we hope to explore other instances of single-spin quantum dynamics involving either larger values of spin or the extension of classical continuous-spin models to quantum-rotor models. The quantum dynamics of mobile holes in a frustrated Ising background is discussed in Ref. 15.
  • 22
    • 85038347353 scopus 로고    scopus 로고
    • For some work on one-dimensional models, see B. K. Chakrabati, A. Dutta, and P. Sen, Quantum Ising Phases and Transitions in Tranverse Ising Models (Springer-Verlag, Berlin, 1996)
    • For some work on one-dimensional models, see B. K. Chakrabati, A. Dutta, and P. Sen, Quantum Ising Phases and Transitions in Tranverse Ising Models (Springer-Verlag, Berlin, 1996).
  • 42
    • 85038339889 scopus 로고    scopus 로고
    • We note that the existence of a dimer mapping has interesting topological consequences (Ref. 22), which however will not be discussed in this work
    • We note that the existence of a dimer mapping has interesting topological consequences (Ref. 22), which however will not be discussed in this work.
  • 43
    • 85038319473 scopus 로고    scopus 로고
    • We thank David Huse for a useful discussion of this point
    • We thank David Huse for a useful discussion of this point.
  • 44
    • 0000955940 scopus 로고
    • This is related to the fact that in layered, ferromagnetically stacked frustrated magnets, fluctuations will determine which state is selected as the ground state in the limit (Formula presented) The importance of fluctuations for such stacked magnets was pointed out by S. N. Coppersmith, Phys. Rev. B 32, 1584 (1985). In our formulation, fluctuations are naturally included and the mapping to the stacked magnets provides a formal connection between these results.
    • (1985) Phys. Rev. B , vol.32 , pp. 1584
    • Coppersmith, S.N.1
  • 45
    • 85038320154 scopus 로고    scopus 로고
    • More precisely, the graph on which hopping occurs can be defined as a high dimensional but finite lattice. For a system of N spins, it is a subgraph of an N-dimensional hypercube
    • More precisely, the graph on which hopping occurs can be defined as a high dimensional but finite lattice. For a system of N spins, it is a subgraph of an N-dimensional hypercube.
  • 51
    • 85038323576 scopus 로고    scopus 로고
    • Note that the columnar dimer state is disordered in dimer language as it breaks no symmetries of the lattice. Had the hierarchical state been selected, there would have been breaking of translational symmetry
    • Note that the columnar dimer state is disordered in dimer language as it breaks no symmetries of the lattice. Had the hierarchical state been selected, there would have been breaking of translational symmetry.
  • 52
    • 85038302037 scopus 로고    scopus 로고
    • A phase diagram of the quantum-dimer model with these features has been obtained before, see Refs. 22 and 43
    • A phase diagram of the quantum-dimer model with these features has been obtained before, see Refs. 22 and 43.
  • 60
    • 0004379532 scopus 로고    scopus 로고
    • A. Gervois M. Gingold D. Iagolnitzer IUPAP Commission on Statistical Physics, Paris
    • This mapping was independently noted by C. L. Henley, in Book of Abstracts of STATPHYS 20, edited by A. Gervois, M. Gingold, and D. Iagolnitzer (IUPAP Commission on Statistical Physics, Paris, 1998).
    • (1998) Book of Abstracts of STATPHYS 20
    • Henley, C.L.1
  • 69
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    • Different representations of the ice model are explained in G. T. Barkema and M. E. J. Newman, Phys. Rev. E 57, 1155 (1998).
    • (1998) Phys. Rev. E , vol.57 , pp. 1155
    • Barkema, G.T.1    Newman, M.E.J.2


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