Thermodynamic limit in the elastic triangle: perturbation theory

The equilibrium state of a triangular pile of particles, interconnected by linear springs and subjected to the force of gravity, is explored algebraically. A subset of the springs is treated as weak in relation to the others and perturbation theory is used to obtain the zero order and first order expressions for the equilibrium positions of the particles. The zero order results prove to satisfy a thermodynamic limit. In contrast, the first order results fail to exhibit a thermodynamic limit because the perturbation expansion parameter proves to be a function of the number of rows of particles in the triangle.