Condensation of an ideal gas obeying non-Abelian statistics

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.

Figure 1

Maximum value of fugacity of an ideal non-Abelian gas as a function of fractional parameter.

Figure 2

Thermodynamic curvature of an ideal non-Abelian gas as a function of fugacity for isotherm processes $(\beta =1,D/\sigma =3/2)$. $R$ is singular at $z=z_{\max }$ for fractional parameter in the interval $0⩽\alpha ⩽0.25.$

Figure 3

Particle number of an ideal non-Abelian gas with different fractional parameter (red solid line, $\alpha =0.05$; blue dashed line, $\alpha =0.1$; green dash-dotted line, $\alpha =0.2$; and purple dotted line, $\alpha =0.4$) as a function of fugacity for isotherm processes. $(\beta =1,D/\sigma =3/2).$

Figure 4

The derivative of particle number of an ideal non-Abelian gas with different fractional parameter (red solid line, $\alpha =0.05$; blue dashed line, $\alpha =0.1$; green dash-dotted line, $\alpha =0.2$; and purple dotted line, $\alpha =0.4$) as a function of fugacity for isotherm processes. $(\beta =1,D/\sigma =3/2).$

Figure 5

Phase transition temperature as a function of fractional parameter for nonrelativistic particles in $(D=3)$ (blue square symbols) and $(D=2)$ (red diamond symbols). $B=\frac{k_B\pi }{a{h}^2{n}^{2/D}}$ is a constant.