Two-Dimensional Frustration Modeling*

Frustration results from competing and random interactions among spins, atoms or characters generally. Computationally, we study frustrated systems like (spin) glasses, and amorphous solids. We define frustration of a character to be proportional to the square of the distance between the actual and assigned positions. This frustration model is similar to an Ising model and comparable to a set of harmonic oscillators.
The total time-dependent frustration is recorded, as characters move to relax and minimize their frustration in a two-dimensional lattice. Using Monte Carlo simulations, frustration is studied for different numbers of characters and assigned distances. Characters assigned to regular structures like Thomson Figures show exponential relaxation. For characters with random assignments, power relaxation is seen.
For characters where the assignments are to form a chain, we observe unexpected behavior. Initially, the frustration relaxes exponentially to zero. Yet, the frustration then jumps up, after which it relaxes to zero while the chain is formed. Our frustration modeling may enable a better understanding of glasses and glassy structures. A thriving glass technology could be a potential outcome.