In a concentrated solution of radical molecules — each carrying an unpaired electron spin — random thermal collisions produce momentary exchange interactions. The first-order contribution from these collisions averages to zero. The radicals tumble randomly, approach from random directions, and the exchange coupling flips sign often enough that its mean contribution vanishes.
The second-order contribution survives.
The stochastic collision theory developed here shows that when two radicals collide, the exchange interaction during the collision creates a transient spin correlation. When the same radical later collides with a third, the correlation from the first collision influences the outcome of the second. This pair-mediated process produces a net ferromagnetic coupling that does not average away, because it depends on the square of the exchange interaction — always positive — rather than the first power.
The mechanism bridges two scales that usually live in separate theories. Stochastic molecular collisions are a kinetic-theory object — Boltzmann statistics, mean free paths, collision frequencies. Ferromagnetic ordering is a condensed-matter object — mean-field theory, critical temperatures, spontaneous magnetization. The collision theory connects them: macroscopic magnetism emerges from the statistical residue of microscopic random events.
The surviving coupling is weak — proportional to the square of the exchange integral divided by the thermal energy — but it is always there in any sufficiently concentrated radical fluid. The question is whether the resulting effective Curie temperature is accessible experimentally. For typical organic radicals, probably not. For systems with large exchange integrals (metal-organic radicals, heavy-element complexes), possibly.
The zeroth lesson: when the mean vanishes, look at the variance. The signal lives in the fluctuations.