Novel Synthesis Method II · 2026

Ising Model
Sound Synthesis

Statistical mechanics as an audio engine. A 2D lattice of magnetic spins undergoes a phase transition at critical temperature Tc=2.269 — producing 1/f noise, the natural spectrum of music.

2.27
Temperature T
0.00
Magnetization
0.00
Energy /site
Critical
Phase
Spin Lattice · ↑ +1 / ↓ −1 (click to flip domain)
128×128 · METROPOLIS
Phase Space · click to jump temperature
← Ferromagnetic · Tc=2.269 · Paramagnetic →
Physics Parameters
2.27
Tc
Critical
Audio Readout
Mode
Sound Shaping
LFO → Temperature Modulation
Reverb
Delay
Metropolis Algorithm · 2D Ising Model
ΔE = 2·s[i,j] · (J·Σneighbours + H)   (anisotropic: Jx ≠ Jy)
P(flip) = 1 if ΔE < 0,  else exp(−ΔE / T)

At T = Tc ≈ 2.269 (in units of J/k_B), the system undergoes a second-order phase transition. Spin correlation length diverges → 1/f power spectrum → the statistical fingerprint of music, language, and heartbeats. J sets coupling strength · H is external field · row magnetization is read as audio waveform.