an expression independent of the detail of random average, this approach is easily extended \[19\] for describing continuous glass transitions \[15\] induced by correlated disorder. On the other hand, it is unclear at present to what extent this approach can be extended into the resulting glass phases.

In this article, a theoretical development on the vortex glass transitions based on eq.(1.1) is reviewed. Consistently with eq.(1.1), the GL model for the layered system, i.e., the Lawrence-Doniach (LD) model \[23\], will be used throughout this paper: $${\cal H}_{\rm LD}=d \sum_j \int d^2r \biggl[ \, \biggl({T \over
{T_{c0}}}-1\biggr) |\psi_j|^2 + \xi_0^2 \biggl|\biggl(-{\rm
i}\nabla_\perp + {{2\pi} \over {\phi_0}} {\bf A}_{\perp, j} \biggr)
\psi_j \biggr|^2$$ $$+ \Gamma^{-1} \biggl({{\xi_0} \over d}\biggr)^2 \biggl|\psi_j -
\psi_{j+1}
\exp{\biggl({\rm i} {{2\pi d {\delta A_\parallel}} \over {\phi_0}}
\biggr)}
\biggr|^2 + {b \over 2} |\psi_j|^4 \biggr] \eqno(1.2)$$ with disorder terms $${\cal H}_{rp}=d \sum_l \int d^2r \biggl[ \, u_l({\bf r})
|\psi_l({\bf r})|^2 + f_l({\bf r}) \xi_0^2 (\nabla \times {\bf
j}_l)_\parallel \biggr], \eqno(1.3)$$ where $\xi_0$ the in-plane coherence length, $\phi_0$ the flux quantum, $b > 0$, $\Gamma$ the mass anisotropy, and the vector indices $\perp$ and $\parallel$ imply the directions, respectively, parallel and perpendicular to the layer plane. Throughout this paper, internal gauge 