Anisotropic three-dimensional XY model and vortex-loop scaling

Shenoy, Subodh R. ; Chattopadhyay, Biplab (1995) Anisotropic three-dimensional XY model and vortex-loop scaling Physical Review B: Condensed Matter and Materials Physics, 51 (14). pp. 9129-9147. ISSN 1098-0121

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Scaling equations are obtained for thermally excited vortex loops in the anisotropic three-dimensional (3D) XY model with interplane/intraplane coupling ratio K/K||0−2. For high-Tc superconductors, γ0−2, related to the Ginzburg-Landau masses, is in a strong anisotropy regime, γ0−1 < 0.5, and a length scale r00a0 naturally arises (a0= lattice constant). (i) For loop major axes a > r0, the dominant excitations are 3D elliptical vortex loops cutting multiple planes, with a~ξ_(T)=a0||ε||−ν where ||ε||≡||(T-Tc)/Tc||, and ν=0.67. The vorticity segment components (μ=x^,y^,z^) are Jμ(r)=0,±1, and interact via a Biot-Savart-like law. The renormalized anisotropy γl−1→1, asymptotically isotropic, as l=ln(a/a0)→∞: anisotropy is irrelevant. (ii) For loop scales r0 > a > 2a0 the dominant excitations are quasi-2D rectangular loops with short sides Jz(r)=±1 cutting single planes, that are thus effectively decoupled at finite scales < r0. The Jz=±1 vortex components, of in-plane separation ||R→WmN|| < r0, interact via a logarithmic [ln(||R→||||/r0)] plus linear [Q0(||R→||||/a0-1)] potential. As γ0−1→0, the coefficient Q0→0, and the Kosterlitz-Thouless limit is recovered. (iii) The 3D transition temperature Tc versus K/K||, calculated for strong anisotropies from "2D" (3D) scaling for scales < r0 (> r0), matches existing Monte Carlo data well. Critical regions ||εc||=||≤γ0−1/ν are estimated. Contact is made with ideas of an intrinsic critical current arising from linear ~γ0−1R|| vortex segment effective potentials.

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