Avoided critical behavior in a uniformly frustrated system

Physica A: Statistical Mechanics and its Applications

Volumn 225, Issue 1, 1996, Pages 129-153

  Chayes, L ^a   Emery, V J ^b   Kivelson, S A ^a   Nussinov, Z ^a   Tarjus, G ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b BROOKHAVEN NATIONAL LABORATORY   (United States)

^c UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Avoided critical point; Spherical spin model; Uniform frustration

Indexed keywords

EID: 0042038997     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/0378-4371(95)00374-6     Document Type: Article

References (24)

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7. D. Wu, D. Chandler and B. Smit, J. Phys. Chem. 96 (1992) 4077; see also, F.H. Stillinger, J. Chem. Phys. 78 (1983) 4654; An lsing version of the present model with a screened Coulomb interaction was considered in H-J. Woo, C. Carraro and D. Chandler (unpublished).
8. D. Wu, D. Chandler and B. Smit, J. Phys. Chem. 96 (1992) 4077; see also, F.H. Stillinger, J. Chem. Phys. 78 (1983) 4654; An lsing version of the present model with a screened Coulomb interaction was considered in H-J. Woo, C. Carraro and D. Chandler (unpublished).
9. D. Wu, D. Chandler and B. Smit, J. Phys. Chem. 96 (1992) 4077; see also, F.H. Stillinger, J. Chem. Phys. 78 (1983) 4654; An lsing version of the present model with a screened Coulomb interaction was considered in H-J. Woo, C. Carraro and D. Chandler (unpublished).
10. See, M.E. Fisher, J. of Stat. Phys. 75 (1994) 1, and references therein.
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13. Z. Nussinov and J. Rudnick, work in progress.
14. xy. At finite temperature, of course, there are no ordered phases. The quantum spherical model defined as in the present paper has precisely these phases, in addition to a zero-temperature quantum disordered phase.
15. p = 1.
16. 1 is the Lagrange multiplier for the first spin-flavor. At the end of the day, this makes the model of Nieuwenhuizen equivalent to the special, degenerate case of our model in which the classical and quantum pieces of the Hamiltonian in Eq. (1.8) are equal and hence the only possible ordered phase is the supersolid phase.
17. J.W. Hartman and P.B. Weichman, Phys. Rev. Lett. 74 (1995) 4584. This paper deals with a large n generalization of a model of rigid rotors. In the usual language of superconductivity, the angular momentum of the rotor is identified with the local particle density, so the kinetic energy is the (short-ranged) Coulomb interaction between particles, while ordering of the rotor coordinate is identified with superconducting order. For this reason, in making comparison with the model in the present paper, we have performed a canonical transformation interchanging the momenta and coordinates of Hartman and Weichman. Since in the original language, the constraint equation involved the spin coordinates alone, after this transformation it involves the momenta only. See also, Y. Tu and P.B. Weichman, Phys. Rev. Lett. 73 (1994) 6.
18. J.W. Hartman and P.B. Weichman, Phys. Rev. Lett. 74 (1995) 4584. This paper deals with a large n generalization of a model of rigid rotors. In the usual language of superconductivity, the angular momentum of the rotor is identified with the local particle density, so the kinetic energy is the (short-ranged) Coulomb interaction between particles, while ordering of the rotor coordinate is identified with superconducting order. For this reason, in making comparison with the model in the present paper, we have performed a canonical transformation interchanging the momenta and coordinates of Hartman and Weichman. Since in the original language, the constraint equation involved the spin coordinates alone, after this transformation it involves the momenta only. See also, Y. Tu and P.B. Weichman, Phys. Rev. Lett. 73 (1994) 6.
19. k → √WQ as k → 0, which has a natural interpretation as the plasma mode.
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22. See, for example, A. Aharony, Y. Imry and S.K. Ma, Phys. Rev. Lett. 37 (1976) 1364; A.P. Young, J. Phys. C 10 (1977) L257; G. Parisi and N. Sourlas, Phys. Rev. Lett. 43 (1979) 744.
23. See, for example, A. Aharony, Y. Imry and S.K. Ma, Phys. Rev. Lett. 37 (1976) 1364; A.P. Young, J. Phys. C 10 (1977) L257; G. Parisi and N. Sourlas, Phys. Rev. Lett. 43 (1979) 744.
24. See, for example, A. Aharony, Y. Imry and S.K. Ma, Phys. Rev. Lett. 37 (1976) 1364; A.P. Young, J. Phys. C 10 (1977) L257; G. Parisi and N. Sourlas, Phys. Rev. Lett. 43 (1979) 744.