Simulating the 3D Ising model
A simulation of the three-dimensional Ising model, implemented with two different sampling strategies so their behaviour can be compared directly:
- Simulated annealing — single-spin updates under a temperature schedule that is gradually lowered towards the ground state.
- The Wolff algorithm — a cluster method that flips whole correlated regions of spins at once. This matters near the critical temperature, where single-spin methods suffer from critical slowing down and the correlation time blows up; flipping clusters largely avoids that.
The Ising model is the standard testbed for phase transitions in statistical physics, and the contrast between a local and a cluster update rule is a clean illustration of why algorithm choice, not just compute, determines whether a simulation is usable near criticality.