Holographic description of chiral symmetry breaking in a magnetic field in 2+1 dimensions with an improved dilaton

We consider a holographic description of the chiral symmetry breaking in an external magnetic field in $(2+1)$ -dimensional gauge theories from the softwall model using an improved dilaton field profile given by $\Phi(z) = - kz^2 + (k+k_1)z^2\tanh (k_{2}z^2)$ . We find inverse magnetic catalysis for B Bc, where Bc is the pseudocritical magnetic field. The transition between these two regimes is a crossover and occurs at $B=B_c$ , which depends on the fermion mass and temperature. We also find spontaneous chiral symmetry breaking (the chiral condensate $\sigma \not=0$ ) at T = 0 in the chiral limit ($m_q\to 0$ ) and chiral symmetry restoration for finite temperatures. We observe that changing the k parameter of the dilaton profile only affects the overall scales of the system such as Bc and σ. For instance, by increasing k one sees an increase of Bc andσ. This suggests that increasing the parameters k1 and k2 will decrease the values of Bc and σ