Potts-Percolation-Gauss Model of a Solid

TL;DR

This paper introduces a statistical mechanics model of a solid where atomic bonds can fail or survive based on energy thresholds, analyzing phase transitions and thermodynamic properties using renormalization-group and Monte-Carlo methods.

Contribution

It presents a novel Potts-percolation-Gauss model for solids, combining percolation and Gaussian interactions, with detailed phase diagram and thermodynamic analysis.

Findings

Identified phase transition boundaries in the model

Calculated thermodynamic quantities like free energy and cluster sizes

Demonstrated the model's applicability to solid behavior

Abstract

We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian springs. If the energy is larger than a threshold the "spring" is more likely to fail, while if the energy is lower than the threshold the spring is more likely to be alive. The phase diagram and thermodynamic quantities, such as free energy, numbers of bonds and clusters, and their fluctuations, are determined using renormalization-group and Monte-Carlo techniques.