Statistical thermodynamics of ordering systems

Abstract
A statistical thermodynamic approximation for cooperative phenomena in Ising and Heisemberg systems has been developed. Description of order-disorder transformation in alloys as well as evaluation of the magnetic contribution for the free energy of ferromagnets is provided with this approach. The constant coupling approximation is improved by introducing a second pairs reactions after averaging atomic groups, on the analogy of block construction in renormalization group techniques. Temperature variation after renormalizing is taken into account by two suitable temperature functions. As analytic expression for the system free energy is obtained which gives well approximate thermodynamic quantities (order parameter, internal energy, specific heat). In particular, the critical behaviour is properly described, with accurate thermodynamic quantities and right exponents. This approach has been applied to real system, showing what are the differences with ideal Ising system. In order-disorder alloys like β-brass, order parameter and specific heat as a function of temperature are obtained and ordering phenomena are discussed.