Frustration Modeling of Particle Chains*

Frustration is a phenomenon due to competing interactions between particles, spins, charges, or in general, characters.  In a 2D grid, we define Frustration (Frus) as the square of the difference between actual and assigned particle distances.  [1,2].  We assign distances for each particle so that the total Frus is zero, when the particles are in a chain.  This simulation is analogous to the behavior of chained harmonic oscillators.  Particles can make each time discrete steps in their Moore neighborhoods.  Our Python Frus code is based upon earlier Basic Frus modeling.  [1,2]  From a random position and at 0K, each particle moves to decrease its local Frus.  We record the total Frus of the chain over time.  Ghorbani et al [2] reported that at later times, Frus unexpectedly jumped above zero before settling again to zero.  We observe no such anomaly:  Frus decreases monotonically to (and remains) zero.  These anomalies [2] may be a (Basic compiler) bug, related to limited precision of Frus differences.  We find, as the particles settle into a chain, Frus decreasesfollowing closely a logarithmic decay with 2 & 3 particles;  yet, a Frus(t) exponential relaxation appears best for 7 particles.  In most cases, chains are formed, except for 7 particles,  which sometimes settle in non-zero Frus minima.

[1] I M Suarez et al   Effects of Frustration:  a Computational study;    Woodward Conf (1990)          https://doi.org/10.1007/978-1-4612-3440-1_10    

[2] E Ghorbani et al  HUIC Hawaii Int STEM Conf (June 2019) & references therein.