Equation of State of a Solid: Potts-Percolation Model

We include stress and strain in a Potts-percolation model of a solid, see J. Phys.: Condens. Matter 20, 075222 (2008) and Phys Rev E80, 031116 (2009). Neighboring atoms are connected by a bond of Lennard-Jones energy. If the energy is larger than a threshold the bond is more likely to fail, while if the energy is lower than the threshold the bond is more likely to be alive. We compute the equation of state: stress as function of strain and temperature by using renormalization group and Monte Carlo simulations. The phase diagram and the equation of state are determined. When the Potts heat capacity is divergent the continuous transition is replaced by a weak first-order transition through the van der Waals loop mechanism. When the Potts transition is first order the stress exhibits a large discontinuity as function of the strain.