Millimeter-wave networks have already been successfully rolled out in many countries and now the research direction heads toward new technologies and standards to enable Tbps rates for future sixth-generation (6G) wireless communication systems. This work studies a point-to-point terahertz (THz) communication network exploiting the concept of a fluid antenna system (FAS) over correlated alpha-mu fading channels, nicely fitting the THz communication. Furthermore, the considered system is expanded to the selection-combining-FAS (SC-FAS) and maximum-gain-combining- FAS (MGC-FAS) diversity variates at the receiver side. The proposed FAS and its diversity configuration techniques are aimed to combat the high path loss, blockages, and molecular absorption effect related to the THz band. Our contribution includes comprehensive outage probability (OP) performance analysis for the THz band given the non-diversity and diversity FAS receivers. Moreover, the derived outage probability formulas are verified via Monte Carlo simulations. Numerical results have confirmed the superior performance of the MGC-FAS scheme in terms of OP. Finally, this work justifies that a higher number of antenna ports dramatically improves the system performance, even in the presence of correlation.