From Single Molecules to Emergent Behavior
Each site is a two-state molecule that can be OFF or ON. With no neighbor interaction, the molecules fluctuate independently. Turn on neighbor coupling and the same simple molecules can organize collectively into patches and eventually large-scale order.
Fraction ON
0.50
Neighbor agreement
0.50
Interaction / noise J/T
0.50
Global order |m|
0.00
Interpretation
Domains emerging
A Local Rule Produces a Collective Pattern
Local Order Versus Global State
What does temperature mean here?
In this reduced model, T is best interpreted as the strength of random thermal fluctuations or biological noise relative to the interaction energy.
High T lets random flips overwhelm neighbor coupling. Low T lets the interaction J dominate, so matching states persist and collective order emerges.
The useful quantity to watch is therefore the competition between J and T, not temperature alone.