August 2017 | By Tom Power

A sonic implementation of the XY Model from condensed matter physics


The XY Synth is a sonic implementation of the XY Model from Condensed Matter Physics. The XY Model consists of a square 2d lattice of atomic spins. Each atom can have a spin which lies in any direction on the unit circle. A Metropolis Monte-Carlo algorithm is used to propagate the system forward. This algorithm sweeps through the system to decided how to line up the atomic spin vectors.

The sliders give control over the Temperature, Interaction Term and the external field of the system. The visualisation gives an indication of the various possible states of the system; Domains of similar spin can be seen forming. Huge worms which wind their way across the screen. Vortices of spin like eddies of the surface of water can appear.

The corresponding music is designed to accompany the visuals. The distortion of the drone is related to the temperature. The Harmonicity and modulation index of the FM synth are related to the interaction term. The modulation depth is mapped to the external magnetic field.