Figure 1

The zero temperature phase diagram of our phenomenologically deformed D3/D5 system at nonzero (fixed) density, magnetic field, and simulated control parameter $O$ of dimension $\Delta$. The shaded region indicates the chirally symmetric phase and the white region the broken phase. For $\Delta <2$, there is a line of holographic BKT transitions at the critical magnetic field $B_c=\tilde{d}/\sqrt{7}$. There is also a line of second-order quantum critical points triggered by $O$ that connects to the line of BKT transitions. The position of the line depends on the precise manner we introduce $O$. Indeed, the left line corresponds to the choice $\Delta =5/4$ and the right to $\Delta =1$. However, the critical exponents are only a function of the magnetic field and density (Fig. 2). The static critical exponent $\beta$ takes the mean-field value $1/2$ for the solid portion of the lines, but takes on a non-mean-field value for the dotted section as in Eq. (1). The line of critical points then interpolates between a second-order mean-field transition and a holographic BKT transition.Reuse & Permissions

Figure 2

The critical exponent $\beta$ in the deformed D3/D5 system as a function of magnetic field at $\Delta =1$ and $\Delta =5/4$. For small magnetic fields—such that ${\Delta }_{\mathrm{IR}}>3/4$—the exponent $\beta$ assumes a mean-field value, while for larger magnetic fields it does not. The exponents for $\Delta =1$ (blue circle) and $\Delta =5/4$ (red cross) match each other and our prediction (dotted line), Eq. (62), within our numerical accuracy.Reuse & Permissions

Figure 3

The BKT transition in the D3/D5 system with quark density and magnetic field present. (a) The embedding $L$ of a D5 brane in the D3 geometry for various $B=\tilde{d}$ showing the BKT transition. (b) A plot of the quark condensate $c$ versus $B$ across the D3/D5 BKT transition.Reuse & Permissions

Figure 4

The zero temperature “phase diagram” of the deformed D3/D5 theory at zero magnetic field as a function of the dimension and value of the deformation $O$. The shaded region is the chirally symmetric phase and the white is the broken phase. The line of transitions is second-order with mean-field exponents, excepting a holographic BKT transition at $\Delta =2$.Reuse & Permissions

Figure 5

The condensate in the deformed D3/D5 theory at zero magnetic field and $\Delta =1$. The solid line is numerical data and the dotted line a fit. Near the transition the condensate scales with a mean-field exponent, $c\sim \sqrt{O-O_c}$.Reuse & Permissions

Figure 6

The condensate in the deformed D3/D5 system at zero (solid line) and small (dashed line) temperature $\pi T={10}^{-5}\sqrt{\tilde{d}}$, large magnetic field $B=0.98B_c$, and the choice $\Delta =1$. The non-mean-field scaling at zero temperature is destroyed even at this small temperature. The nonzero temperature condensate asymptotes to the zero temperature value far away from the transition.Reuse & Permissions

Figure 7

A log-log plot of the difference of free energy $\Delta F$ in the broken phase at zero temperature as a function of $O$. The dots indicate numerical data at magnetic field $B=0.95B_c$ and the choice $\Delta =1$, and the line a numerical fit. The free energy scales as $\Delta F\sim -(O-O_c{)}^{3.38}$ in the broken phase.Reuse & Permissions