# About Holographic Model of Magnetism and Superconductor

I have a question about this paper http://arxiv.org/abs/1003.0010 In their model, when consider holographic paramagnetic-ferromagnetic phase transition, they need Yang-Mills field itself to condensate. In bulk the Yang-Mills field which is dual to spin wave has the following form $$A^3_t=\mu \alpha(r),~~\alpha(r\rightarrow\infty)=1$$ where the $\mu$ is dual to boundary magnetic field.

When consider holographic paramagnetic-antiferromagnetic phase transition, they focus on the adjoint representation scalar field $\Phi$ which is dual to order parameter of field theory. Near the boundary, the scalar has the following form $$\Phi=A r^{\Delta-3}+B r^{-\Delta},~~ \Delta=\frac{3}{2}+\sqrt{m^2R^2+\frac{9}{4}}$$ When considering holographic paramagnetic-antiferromagnetic phase transition, the authors choose the standard quantization condition where $A=0$ and $B\neq 0$.

My questions are: 1) If $A\neq0$, is this condition dual to paramagnetic-antiferromagnetic phase transition with external field? why do people general not care such case? 2) Also in holographic superconductor models, why do people always require standard/alternatve quantization? why not consider cases with classic current, that is both components are not zero?

Depending on the mass region of $\Phi$, either A or B can be taken as source and the corresponding response (vev). If $B\neq 0$ when $A=0$, it means that the system can spontaneously have a nontrivial vev even without any source. That indicates a phase transition. In the case both $A\neq 0$ and $B\neq 0$, it doesn't mean any phase transition. If we treat $\Phi$ as a fluctuation, $G_R= B/A$ means some kinds of susceptibility.
• how about the system has a vev with some source, that is $A \neq 0$ and $B \neq 0$ ? how to conclude that "it doesn't mean any phase transition."? Naively from the duality, $B$ corresponds to the order parameter in standard quantization. That $B$ varies from zero to nonzero means a phase transition in field theory. Jun 12, 2012 at 3:24