Instability of a magnetized QGP sourced by a scalar operator

We use the gauge/gravity correspondence to study the thermodynamics of a magnetized quark-gluon plasma in the presence of a scalar operator of dimension Δ = 2. We proceed by working in a five-dimensional gauged supergravity theory, where we numerically construct an asymptotically AdS₅ background that describes a black D3-brane in the presence of a magnetic and a scalar fields. We study the asymptotic behavior of the background and its fields close to the AdS₅ region to latter perform a thermodynamic analysis of the solution that includes the renormalization of the free energy associated to it. We find that because of the presence of the scalar operator, there exists a maximum intensity for the magnetic field that the plasma can hold, while for any given intensity smaller than that value, there are two states that differ in their vacuum expectation value for the scalar operator. We show that one of the two branches just mentioned is thermodynamically favored over the other.