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Volumn 57, Issue 2, 1998, Pages 1335-1346

Complex-temperature partition function zeros of the Potts model on the honeycomb and kagomé lattices

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EID: 0002442195     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.1335     Document Type: Article
Times cited : (28)

References (68)
  • 3
    • 0031558825 scopus 로고    scopus 로고
    • These authors use the symbol [Formula Presented] for what is denoted [Formula Presented] here. JPHAC5
    • I. Jensen, A. J. Guttmann, and I. G. Enting, J. Phys. A30, 8067 (1997). These authors use the symbol u for what is denoted z here.
    • (1997) J. Phys. A , vol.30 , pp. 8067
    • Jensen, I.1    Guttmann, A.J.2    Enting, I.G.3
  • 6
    • 85037194663 scopus 로고    scopus 로고
    • M. E. Fisher, Lectures in Theoretical Physics (University of Colorado Press, Boulder, CO, 1965), Vol. 7C, p. 1
    • M. E. Fisher, Lectures in Theoretical Physics (University of Colorado Press, Boulder, CO, 1965), Vol. 7C, p. 1.
  • 14
    • 85037182738 scopus 로고    scopus 로고
    • The free energy also has an isolated singularity at [Formula Presented] and (see theorem 6 of Ref. c11) for the Ising model on lattices with odd coordination number, a singularity at [Formula Presented]. The latter lies on the complex-temperature phase boundary for the honeycomb lattice but is isolated for the heteropolygonal [Formula Presented] lattice
    • The free energy also has an isolated singularity at|K|=∞ and (see theorem 6 of Ref. 11) for the Ising model on lattices with odd coordination number, a singularity at z=-1. The latter lies on the complex-temperature phase boundary for the honeycomb lattice but is isolated for the heteropolygonal 3⋅122 lattice.
  • 16
    • 85037202243 scopus 로고    scopus 로고
    • As discussed in Ref. c14, the complex-temperature extension of a physical phase is obtained by analytically continuing the free energy from the interval of physical temperature to a maximal region allowed by nonanalytic boundaries. Henceforth, we shall generally take the adjective “complex-temperature extension” as implicit when referring to phases. There are also other complex-temperatures that have no overlap with any physical phase; we shall denote these by O for “other.”
    • As discussed in Ref. 14, the complex-temperature extension of a physical phase is obtained by analytically continuing the free energy from the interval of physical temperature to a maximal region allowed by nonanalytic boundaries. Henceforth, we shall generally take the adjective “complex-temperature extension” as implicit when referring to phases. There are also other complex-temperatures that have no overlap with any physical phase; we shall denote these by O for “other.”
  • 43
    • 85037203415 scopus 로고    scopus 로고
    • For the physical critical point, one does not have to distinguish between the exponents [Formula Presented], [Formula Presented] describing the approach from the high-temperature and low-temperature sides, since these are equal
    • For the physical critical point, one does not have to distinguish between the exponents α and α′ describing the approach from the high-temperature and low-temperature sides, since these are equal.
  • 45
    • 85037255817 scopus 로고    scopus 로고
    • both the honeycomb and kagomé cases, the respective conditions (3.1) and (4.1) are the conditions that [Formula Presented], where [Formula Presented] occurs in the term [Formula Presented] in the free energy, and [Formula Presented]. The range of [Formula Presented] is then [Formula Presented], as given
    • In both the honeycomb and kagomé cases, the respective conditions (3.1) and (4.1) are the conditions that L(a, p)=0, where L occurs in the term ∝∫02πdθ1∫02πdθ2ln[L(a, p)] in the free energy, and p=cos(θ1)+cos(θ2)+cos(θ1+θ2). The range of p is then -3/2
  • 46
    • 85037212574 scopus 로고    scopus 로고
    • By duality, for the Ising model on the honeycomb lattice, [Formula Presented] in the [Formula Presented] plane is the same as [Formula Presented] in the [Formula Presented], [Formula Presented] plane for same model on the triangular lattice c31. Note that for the case of anisotropic spin-spin couplings, the partition function zeros fill out regions rather than lying on curves in the [Formula Presented] plane c34
    • By duality, for the Ising model on the honeycomb lattice, B in the a plane is the same as B in the ad=(a+1)/(a-1) plane for same model on the triangular lattice 31. Note that for the case of anisotropic spin-spin couplings, the partition function zeros fill out regions rather than lying on curves in the a plane 34.
  • 50
    • 0042715204 scopus 로고    scopus 로고
    • J. Stephenson, 148A, 107 (1988) and references therein
    • J. Stephenson, 148A, 107 (1988) and references therein.
  • 51
    • 84953710796 scopus 로고
    • Princeton University Press, Princeton
    • S. Lefschetz, Algebraic Geometry (Princeton University Press, Princeton, 1953);
    • (1953) Algebraic Geometry
    • Lefschetz, S.1
  • 58
    • 0037923007 scopus 로고
    • Fig. 1717, Academic Press, New York, C. Domb, M. S. Green
    • see also Fig. 1717 in E. H. Lieb and F. Y. Wu, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic Press, New York, 1972), p. 331.
    • (1972) Phase Transitions and Critical Phenomena , pp. 331
    • Lieb, E.H.1    Wu, F.Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.