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We study the thermodynamics of AdS-Schwarzschild black hole in the presenceof an external string cloud. We observe that, at any temperature, the blackhole configuration is stable with non-zero entropy. We further notice that,when the value of the curvature constant equals to one, if the string clouddensity has less than a critical value, within a certain range of temperaturethree black holes configuration exist. One of these black holes is unstable andother two are stable. At a critical temperature, a transition between these twostable black holes takes place which leads us to conclude that the bound stateof quark and anti-quark pairs may not exist. By studying the corresponding dualgauge theory we confirm that the instability of the bound state of quark andanti-quark pair in the dual gauge theory.

Phase transition of AdS Schwarzschild black hole and gauge theory dual in presence of external string cloud