  We explore the phase transitions of the ideal relativistic neutral Bose gas
confined in a cubic box, without assuming the thermodynamic limit nor
continuous approximation. While the corresponding non-relativistic canonical
partition function is essentially a one-variable function depending on a
particular combination of temperature and volume, the relativistic canonical
partition function is genuinely a two-variable function of them. Based on an
exact expression of the canonical partition function, we performed numerical
computations for up to hundred thousand particles. We report that if the number
of particles is equal to or greater than a critical value, which amounts to
7616, the ideal relativistic neutral Bose gas features a spinodal curve with a
critical point. This enables us to depict the phase diagram of the ideal Bose
gas. The consequent phase transition is first-order below the critical pressure
or second-order at the critical pressure. The exponents corresponding to the
singularities are 1/2 and 2/3 respectively. We also verify the recently
observed `Widom line' in the supercritical region.
