High-$T_c$ and $t$-$J$ model: passions and disappointments

I will discuss the high-temperature phase diagram of the two-dimensional $t$-$J$ and related models. Among the many numerical and analytical techniques which have been used to search for superconductivity in these models, only a few provide unbiased results. Particularly, the high-temperature series constructed for a number of thermodynamical correlation functions indicate that in the accessible range of temperatures, $T\ge J/2$, the superconducting fluctuations are only pronounced in the unphysical regime, $J>t$, while they are strongly suppressed in the physical regime, $J