ANISOTROPIC 3-DIMENSIONAL XY MODEL AND VORTEX-LOOP SCALING

Scaling equations are obtained for thermally excited vortex loops in the anisotropic three-dimensional (3D) XY model with interplane/intraplane coupling ratio K/K=γ0-2. 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 r0=γ0a0 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-ν where (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 c≤γ0-1/ν are estimated. Contact is made with ideas of an intrinsic critical current arising from linear ∼γ0-1R vortex segment effective potentials. © 1995 The American Physical Society.