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Following previous study about AdS-Schwarzschild black holes minimallycoupled to a cloud of strings in the context of massive gravity{Ghanaatian:2019} and inspired by strong connection between Gauss-BonnetGravity and heterotic string theory, in this paper, we first take into accountthe Gauss-Bonnet term and we study thermodynamics and critical behavior ofthese black holes in the extended phase space. The effects of Gauss-Bonnet,massive, and string cloud parameters on the criticality of these black holeshas been investigated. It can be seen that the Gauss-Bonnet and massiveparameters have opposite effects on the criticality and phase transition of thesolutions. We also observe that the increase in the value of the string cloudparameter above a critical value, eliminates the van der Waals like behavior ofthese solutions. Also, the Joule-Thomson effect is not observed. Then weexamine thermal stability of these black holes in canonical ensemble bycalculating the heat capacity. In addition, we explore critical behavior inextended phase space by employing heat capacity and consequently, we observethat the results are in agreement with the previous results from the usualmethod in section 3.

Critical behavior of AdS Gauss-Bonnet massive black holes in the presence of external string cloud