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Video abstract for the article 'Existence of a critical point in the phase diagram of the ideal relativistic neutral Bose gas' by Jeong-Hyuck Park and Sang-Woo Kim (Jeong-Hyuck Park and Sang-Woo Kim 2011 New J. Phys. 13 033003). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/13/3/033003/fulltext/. GENERAL SCIENTIFIC SUMMARY Introduction and background. Quantum mechanics and relativity are two cornerstones of modern physics, and the identical properties of elementary particles is a genuine quantum effect. In order to see the emergent properties of relativistic identical bosonic particles, we explore the phase transitions of a relativistic ideal Bose gas confined in a cubic box, without assuming either thermodynamic limit or continuous approximation. Main results. Based on an exact expression of the canonical partition function, we perform numerical computations up to a hundred thousand particles using a supercomputer. We report that if the number of particles is sufficiently large, which turns out to be the particular number '7616', the ideal gas features a spinodal curve with a critical point, which enables us to depict its phase diagram. The consequent phase transition is first order below critical pressure, and second order at critical pressure. The exponents corresponding to the singularities are 1/2 and 2/3, respectively. In particular, we verify the 'Widom line' in the supercritical region, which was observed experimentally recently. Wider implications. The resulting phase diagram is strikingly similar to that of the van der Waals equation of state. Our result may indicate that the main mechanism for the usual liquid--gas phase transition is due to identical properties.