Critical Properties of the $N$-Color London Model

The critical properties of the $N$-color London model are studied in $d=2+1$ dimensions. The model is dualized to a theory of $N$ vortex fields interacting through a Coulomb and a screened potential. The model with $N=2$ shows two anomalies in the specific heat. From the critical exponents $\alpha$ and $\nu$, the mass of the gauge field, and the vortex correlation functions, we conclude that one anomaly corresponds to an inverted $3\mathrm{D}xy$ fixed point, while the other corresponds to a $3\mathrm{D}xy$ fixed point. There are $N$ fixed points, namely, one corresponding to an inverted $3\mathrm{D}xy$ fixed point, and $N-1$ corresponding to neutral $3\mathrm{D}xy$ fixed points. This represents a novel type of quantum fluid, where superfluid modes arise out of charged condensates.

Figure 1

The FSS of the peak-to-peak value of the third moment $\Delta M_3$ labeled (□) and (+) for $T_{\mathrm{c}\mathrm{1}}$ and $T_{\mathrm{c}\mathrm{2}}$ respectively. The scaling of the width between the peaks $\Delta \beta$ labeled ($▴$) and ($\times$) for $T_{\mathrm{c}\mathrm{1}}$ and $T_{\mathrm{c}\mathrm{2}}$, respectively. The lines are power law fits to the data for $L>6$ used to extract $\alpha$ and $\nu$.

Figure 2

$G^{(+)}(q)$ for $N=2$,$L=32$. For $T=2.86>T_{\mathrm{c}\mathrm{2}}$, $T=2.76\simeq T_{\mathrm{c}\mathrm{2}}$, and $T=2.63<T_{\mathrm{c}\mathrm{2}}$, $\underset{\mathbf{q}\mathbf{\to }\mathbf{0}}{lim}{G}^{(+)}(q)\sim c(T)$, $\sim q$, and $\sim q^2$, respectively.

Figure 3

The mass $m_{\mathbf{A}}$ ($⧫$) and $1-m_0/m_{\Sigma \mathbf{h}}$ (+) found from Eq. (7). Two nonanalyticities can be seen in $m_{\mathbf{A}}$ at $T_{\mathrm{c}\mathrm{1}}$ and $T_{\mathrm{c}\mathrm{2}}$, corresponding to a neutral fixed point and a charged Higgs fixed point, respectively. An abrupt increase in $m_{\Sigma \mathbf{h}}$ due to vortex condensation is located at $T_{\mathrm{c}\mathrm{2}}$.