Hidden order in noisy worlds: predicting a warming planet and the physics of disorder

Imagine trying to predict the exact splash of every wave on a beach. Impossible. But you can still say with confidence that the tide will come in. The 2021 physics prize is about telling those two things apart: the wild, unpredictable details and the steady pattern hiding underneath them.

Two of the winners studied the climate. They showed that even though tomorrow's weather is a guess, the planet's average temperature follows clear rules. Pump more carbon dioxide into the air and you trap more heat, so the Earth must warm. That is a pattern you can trust even when the daily weather jumps all over the place.

Earth's temperature is set by a simple accounting rule: energy arriving as sunlight must balance energy leaving as infrared heat. In 1967 Syukuro Manabe and Richard Wetherald captured this in a one-dimensional radiative-convective model, a single vertical column of atmosphere. It tracked how radiation and rising warm air carry heat upward, and crucially it let warmer air hold more water vapour, a feedback that amplifies any nudge.

But why does the climate wobble at all, even without an external push? Klaus Hasselmann answered this in 1976 with a stochastic climate model. He treated fast, random weather like the jittering molecules that buffet a pollen grain in water, and the slow ocean like the heavy grain that accumulates those kicks into lasting drift. Short-term noise, integrated over time, produces long-term climate variability.

Giorgio Parisi worked on a different complex system: spin glasses, alloys with magnetic atoms scattered at random so that their interactions conflict, a situation called frustration. Around 1980 he found an exact solution to a model of these systems, revealing that their many frozen states are organised in a hidden, hierarchical pattern. The method reaches far beyond magnets, into neural networks, optimisation, and machine learning.

Manabe's radiative-convective equilibrium model reduced the atmosphere to a single column in which net radiative heating is balanced by a convective adjustment that relaxes the lapse rate toward a stable profile whenever it would otherwise overturn. The decisive choice was to fix relative rather than absolute humidity, so that warming automatically raises the water vapour column. This closes a positive feedback loop: added CO2 lifts the temperature, warmer air holds more vapour, and vapour is itself a strong infrared absorber. The model yields a climate sensitivity near 2 degrees Celsius per CO2 doubling and predicts simultaneous surface and tropospheric warming with stratospheric cooling, the vertical signature that distinguishes greenhouse forcing from a change in solar output.

Parisi attacked the Sherrington-Kirkpatrick spin glass, the mean-field model of magnets with random, competing couplings. The replica trick computes the disorder-averaged free energy by analysing n copies of the system and taking n to zero, but the naive replica-symmetric solution gives a negative entropy, a clear sign that it is wrong. Parisi's breakthrough was full replica symmetry breaking: an order parameter that is not a single number but an entire function, encoding the probability distribution of overlaps between states. The solution reveals an ultrametric, hierarchically nested organisation of infinitely many pure states separated by extensive energy barriers, a rigid order beneath apparent randomness.

What unites the two halves of the prize is a single stance: in a system with enormous numbers of interacting parts and a heavy dose of randomness, the right move is not to track every detail but to characterise the statistics and name the structure that survives the noise. Manabe and Hasselmann extracted a predictable, forced climate signal from the chaos of weather; Parisi extracted a strict mathematical hierarchy from the frozen chaos of disorder. His order parameter is, in spirit, the same kind of object as Hasselmann's fingerprint, a way to identify the pattern hiding inside fluctuations. Parisi's tools, born for atomic spins, now describe neural networks, optimisation landscapes, structural glasses, and even flocking birds, which is why the citation stretches from atomic to planetary scales. The deep claim of the 2021 prize is that complexity is not the same thing as unpredictability.