🌀 Spin Glass — Frustration & Slow Relaxation

Each bond's colour reflects whether it is currently satisfied given the two spins either side of it and its own fixed random sign. As spins flip during Monte Carlo sweeps, a bond can switch between satisfied (blue) and frustrated (red) even though its underlying coupling strength never changes.

Temperature T sets the probability of accepting a spin flip that increases the total energy, via the factor exp(−ΔE/T). Higher T means more disordering flips are accepted, keeping the lattice close to a random paramagnetic state; lower T makes the system increasingly reluctant to accept unfavourable flips, favouring slow settling into low-energy frustrated configurations.

Because bonds have mixed signs, the energy landscape has many nearly-equal-depth valleys separated by barriers of different heights. Escaping one valley for a deeper one gets progressively harder, so the average energy per site declines in a slow, roughly logarithmic manner instead of dropping quickly to a single ground state.

Moving the Grid size slider (10–50) rebuilds the lattice at the new size and draws a completely fresh set of random bond signs and spin orientations, resetting the sweep counter and energy history. It does not resize the existing lattice in place.

Not in the usual ferromagnetic sense. Because roughly half the bonds are antiferromagnetic, the global magnetisation stays close to zero even at low temperature. What can freeze instead is the order parameter q, which captures whether individual spins settle into a fixed (if random-looking) orientation over time — the hallmark of the spin-glass phase below the freezing temperature.