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

Following previous study about AdS-Schwarzschild black holes minimally coupled to a cloud of strings in the context of massive gravity (Ghanaatian et al. in Effects of the external string cloud on the Van der Waals like behavior and efficiency of AdS-Schwarzschild black hole in massive gravity, [hep-th]) and inspired by strong connection between Gauss-Bonnet Gravity and heterotic string theory, in this paper, we first take into account the Gauss-Bonnet term and we study thermodynamics and critical behavior of these black holes in the extended phase space. The effects of Gauss-Bonnet, massive, and string cloud parameters on the criticality of these black holes has been investigated. It can be seen that the Gauss-Bonnet and massive parameters have opposite effects on the criticality and phase transition of the solutions. We also observe that the increase in the value of the string cloud parameter above a critical value, eliminates the van der Waals like behavior of these solutions. Also, the Joule-Thomson effect is not observed. Then we examine thermal stability of these black holes in canonical ensemble by calculating the heat capacity. In addition, we explore critical behavior in extended phase space by employing heat capacity and consequently, we observe that the results are in agreement with the previous results from the usual method in Sect. 3.