Equation of State from Potts-Percolation Model of a Solid

TL;DR

This paper models the mechanical behavior of a solid using an extended Potts-percolation framework, incorporating stress, strain, and atomic interactions via Lennard-Jones potential, and analyzes phase transitions and material properties.

Contribution

It introduces a novel extension of the Potts-percolation model to include stress and strain, providing a detailed analysis of phase transitions and mechanical properties of solids.

Findings

Equation of state derived from the model

Identification of phase transition types and their effects on stress

Determination of the material's thermal and mechanical properties

Abstract

We expand the Potts-percolation model of a solid to include stress and strain. Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. 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. In two dimensions we compute the equation of state: stress as function of inter-atomic distance and temperature by using renormalization group and Monte Carlo simulations. The phase diagram, the equation of state, the isothermal modulus and the thermal expansion 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 inter-atomic distance.