Novel Numerical Computations for the Equation of State of Hard Particle Systems from Gaseous to Extreme High Densities

A special form of the ``Reduced Monte Carlo Scheme'' (RMCS) used for numerical computation of the EOS of the hard particle system (2D and 3D cases) will be discussed. A major advantage of the numerical scheme is that it does not lead to difficulties with meta-stable states as do traditional MC methods. In particular, RMCS calculations (in the special form) provide results from the lowest (fluid phase) to the highest (solid phase) densities which show a first order phase transition in the hard particle system