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Quantum chromodynamics (QCD) with pure imaginary baryon number chemicalpotential mu =i*theta*T, where T is temperature and theta is a real number, hasthe Roberge-Weiss periodicity. We study the theta-dependence of the baryonnumber density and the pressure in the hadron resonance gas model with excludedvolume effects of baryons. It is found that the baryon number density and thepressure 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 MeV. This temperature is consistent with the Roberge-Weisstransition temperature TRW obtained by lattice QCD simulations. Thissingularity can be explained by the dual excluded volume effects in which theroles of point-like and non point-like particles are exchanged each other inthe ordinary excluded volume effects. It is also indicated that the excludedvolume effect is visible just below TRW and is detectable by the lattice QCDsimulation at finite theta.

Roberge-Weiss periodicity and singularity in hadron resonance gas model with excluded volume effects