Four-dimensional CP$^1+$ U(1) lattice gauge theory for 3D antiferromagnets: Phase structure, gauge bosons and spin liquid

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D.Yoshioka, G.Arakawa, I.Ichinose, and T.Matsui, Phys.Rev. B70
2004
Earlier work this paper cites.
I.Ichinose and T.Matsui, Phys.Rev.Lett. 86
2005
Earlier work this paper cites.

S.Takashima, I.Ichinose, and T.Matsui, Phys.Rev. B72
2005
Cited alongside, same era.
I.Ichinose and T.Matsui, Phys.Rev. B45
2006
Cited alongside, same era.
Derivation of the effective CP 1 model in the continuum limit is discussed in detail in the first paper of Ref. [ 1 ]
Cited in the paper.
T.Hiramatsu and T.Matsui, in preparation
Cited in the paper.
More precisely, we fit the correlator as D G ( y μ , y ν ) ∝ exp ⁡ ( − λ y μ 2 + y ν 2 ) , D_{G}(y_{\mu},y_{\nu})\propto\exp(-\lambda\sqrt{y^{2}_{\mu}+y^{2}_{\nu}}), by adjusting a fitting parameter λ \lambda . Then we define M G M_{\rm G} as M G = sgn ⁡ ( λ 2 − p μ 2 − p ν 2 ) | λ 2 − p μ 2 + p ν 2 | . M_{\rm G}={\rm sgn}(\lambda^{2}-p^{2}_{\mu}-p^{2}_{\nu})\sqrt{|\lambda^{2}-p^{2}_{\mu}+p^{2}_{\nu}|}. It has been verified that negative values of M G M_{\rm G} are finite-size effect. See Refs. [ 5 , 6 ]
Cited in the paper.
I.Ichinose, T.Matsui, and K.Sakakibara, work in progress
Cited in the paper.
Negative values of M G M_{\rm G} in Fig. 8
Cited in the paper.
Nonetheless, for the Abelian gauge-Higgs model in 3D, it was suggested that the across the crossover line certain nonlocal physical quantities like flux-line density exhibit typical behavior of second-order phase transition. See S.Wenzel, E.Bittner, W.Janke, and A.M.J.Schakel, arXiv:0708.0903. We expect similar behavior for the present model S ′ S^{\prime}
Original
Cited in the paper.

S.Takashima, I.Ichinose, and T.Matsui, Phys.Rev. B73
2006
Later among the works it cites.
See, for example, K.S.D.Beach and A.W.Sandvik, Phys.Rev.Lett. 99
2007
Closest in time.