About the Background Simulation
The background is a real-time visualization of the Sherrington-Kirkpatrick (SK) model, a classic model of a spin glass in statistical physics.
Instead of a single system, we simulate 6 identical replicas simultaneously. They all share the same random interaction network (the lines you see), but evolve from different initial states.
As the system cools (using simulated annealing via Metropolis-Hastings dynamics), the phase space shatters into many separate energy valleys—a phenomenon known as Replica Symmetry Breaking (RSB), famously solved by Giorgio Parisi.
- The Nodes (Spins): Each circle is a cluster of 6 tiny dots, representing the spin state (Cyan = +1, Magenta = -1) of the 6 replicas. When they agree, the cluster is uniform. When they fall into different valleys, the cluster is mixed.
- The Edges (Couplings): Mint green lines are satisfied bonds, pink lines are frustrated bonds. Grey lines mean the replicas disagree on whether the bond is satisfied!
- The Matrix: The heatmap in the corner shows the Parisi Overlap Matrix, tracking how similar the 6 replicas are to each other. Bright cyan means two replicas found the exact same valley. Move your mouse to "heat up" the system and watch them jump between valleys.