Quantum chromodynamics (QCD) with pure imaginary baryon number chemical potential $\mu =i\theta T$, where $T$ is temperature and $\theta$ is a real number, has the Roberge-Weiss periodicity. We study the $\theta$-dependence of the baryon number density and the pressure in the hadron resonance gas model with excluded volume effects of baryons. It is shown that the baryon number density and the pressure are smooth periodic functions of $\theta$ at low or high temperature. However, they have singular behavior at $\theta =(2k+1)\pi$ where $k$ is an integer, when $T\sim 211\mathrm{MeV}$. This temperature is consistent with the Roberge-Weiss transition temperature $T_{\mathrm{RW}}$ obtained by lattice QCD simulations. This singularity can be explained by the dual excluded volume effects in which the roles of pointlike and nonpointlike particles are exchanged each other in the ordinary excluded volume effects. It is also indicated that the excluded volume effect is visible just below $T_{\mathrm{RW}}$ and is directly detectable by the lattice QCD simulation at finite $\theta$. We compare the results with the one obtained by the Polyakov-loop extended Nambu–Jona-Lasinio model.

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• Nuclear matter
• QCD phase transitions
• Quantum chromodynamics
• Quark matter
• Quark-gluon plasma