Paramagnetism-ferromagnetism phase transition in a dyonic black hole

Coupling an antisymmetric tensor field to the electromagnetic field in a dyonic Reissner-Nordström-anti–de Sitter black hole background, we build a holographic model for the paramagnetism/ferromagnetism phase transition. In the case of zero magnetic field, the time reversal symmetry is broken spontaneously and spontaneous magnetization happens at low temperatures. The critical exponents are in agreement with the ones from mean field theory. In the case of nonzero magnetic field, the model realizes the hysteresis loop of a single magnetic domain and the magnetic susceptibility satisfies the Curie-Weiss law.

Figure 1

The magnetic moment as a function of temperature. Here the critical temperature is $T_c/\mu \simeq 0.00915$.

Figure 2

Left: The magnetic moment with respect to the external magnetic field $B$ at different temperatures. Right: The magnetic susceptibility as a function of temperature.