Exploiting a semi-analytic approach to study first order phase transitions

In a previous contribution [C. E. Fiore and M. G. E. da Luz, Phys. Rev. Lett. 107, 230601 (2011)] we have proposed a method to treat first order phase transitions at low temperatures. It describes arbitrary order parameter through an analytical expression W, which depends on few coefficients. Such coefficients can be calculated by simulating relatively small systems, hence, with a low computational cost. The method determines the precise location of coexistence lines and arbitrary response functions (from proper derivatives of W). Here we exploit and extend the approach, discussing a more general condition for its validity. We show that, in fact, it works beyond the low T limit, provided the first order phase transition is strong enough. Thus, W can be used even to study athermal problems, as exemplified for a hard-core lattice gas. We furthermore demonstrate that other relevant thermodynamic quantities, as entropy and energy, are also obtained from W. To clarify some important mathematical features of the method, we analyze in detail an analytically solvable problem. Finally, we discuss different representative models, namely, Potts, Bell-Lavis, and associating gas-lattice, illustrating the procedure's broad applicability. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772809]