Nobel Prize in Physics 2021: Climate Models and Disordered Systems

This note covers the Nobel Prize in Physics 2021: who won it, what "complex physical systems" means, how Syukuro Manabe and Klaus Hasselmann built the climate models that let scientists reliably predict global warming, how Giorgio Parisi found hidden order inside disordered materials such as spin glasses, how these two strands of work unfolded from the nineteenth to the twenty-first century, why the discoveries matter, and quick facts for exams.

What was the Nobel Prize in Physics 2021 awarded for?

The Royal Swedish Academy of Sciences awarded the Nobel Prize in Physics 2021 with the overall citation: "for groundbreaking contributions to our understanding of complex physical systems".

In plain words, a complex system is anything made of very many interacting parts whose combined behaviour is hard to predict, even though each part may follow simple physical laws.

The weather, the climate, ordinary glass and a flock of starlings are all complex systems.

The committee split the prize in two: one half went jointly to Syukuro Manabe and Klaus Hasselmann for turning the chaotic climate into something that can be modelled and predicted with confidence, and the other half went to Giorgio Parisi for discovering mathematical order hidden inside apparently random materials.

The official name of the award is the Nobel Prize in Physics, and it was announced on 5 October 2021.

Who are the laureates?

Three scientists shared the 2021 prize, with the climate half divided equally and the disordered-systems half going entirely to one laureate.

Syukuro Manabe

Syukuro Manabe was born on 21 September 1931 in Shingu, Ehime, Japan. At the time of the award he was a senior meteorologist at Princeton University, Princeton, NJ, USA, and he received one quarter of the prize.

In the 1960s he built physical models of Earth's climate, becoming the first scientist to study how radiation balance and the vertical movement of air masses interact, showing that doubling atmospheric carbon dioxide raised global temperature by over 2°C in his model.

Klaus Hasselmann

Klaus Hasselmann was born on 25 October 1931 in Hamburg, Germany. At the time of the award he was at the Max Planck Institute for Meteorology, Hamburg, Germany, and he also received one quarter of the prize.

About a decade after Manabe's work, Hasselmann built a model that links the short-term, chaotic weather to the long-term, predictable climate, and devised methods to spot human "fingerprints" in temperature records.

Giorgio Parisi

Giorgio Parisi was born on 4 August 1948 in Rome, Italy. At the time of the award he was a professor at Sapienza University of Rome, Italy, and he received one half of the prize on his own.

Around 1980 he discovered hidden mathematical patterns inside disordered materials such as spin glasses, work that later influenced mathematics, biology, neuroscience and machine learning.

Why are complex systems so hard to understand?

Many everyday systems are made of huge numbers of particles or parts that move or interact in ways that look random. Physicists had studied this kind of randomness for centuries, but two particular puzzles stood out by the twentieth century.

The first puzzle was Earth's climate. The weather tomorrow is notoriously hard to predict because tiny differences in starting conditions can grow into completely different outcomes within days, a phenomenon popularly called the butterfly effect and formally studied as chaos theory by the American meteorologist Edward Lorenz in the 1960s.

If weather itself is chaotic, it was not obvious why long-term climate predictions, covering decades, should be trustworthy at all.

The second puzzle concerned materials such as spin glasses, metal alloys in which a few iron atoms are mixed at random into a grid of copper atoms.

Each iron atom acts like a tiny magnet, and neighbouring magnets pull against each other in conflicting directions, a situation physicists call frustration.

Nobody had a general mathematical way to describe what pattern such frustrated systems would settle into, or why repeating the same experiment gave a different arrangement each time.

Both puzzles needed a new kind of physics: one that could handle randomness and disorder directly, rather than averaging it away, and still produce reliable predictions about how the system behaves over the long run.

How did Manabe and Hasselmann build climate models that work?

Understanding Earth's temperature starts with the greenhouse effect: sunlight reaches the ground, is converted into infrared ("dark heat") radiation, and some of this heat is trapped by gases in the atmosphere, chiefly carbon dioxide, methane and water vapour, which make up a very small share of the atmosphere by volume.

More carbon dioxide allows the air to hold more water vapour too, creating a feedback loop that raises temperature further.

Manabe's contribution in the 1960s was to build a physical model of this process rather than rely only on radiation balance, as the earlier work of Svante Arrhenius had done around 1896. His approach can be summarised as a sequence of steps:

1. Reduce the atmosphere to a manageable one-dimensional vertical column, roughly 40 kilometres high, to make the calculations possible with the computers of the time.
2. Add the vertical transport of air masses by convection and the latent heat released when water vapour condenses, alongside the radiation balance that earlier models used alone.
3. Run the model repeatedly, varying the level of each atmospheric gas in turn, to see which gas actually changes the surface temperature.
4. Compare the predicted temperature pattern through the atmosphere: if carbon dioxide is the cause, the lower atmosphere should warm while the upper atmosphere cools, a signature different from what extra solar radiation would produce.

This one-dimensional model, published through the 1960s, later grew into a three-dimensional climate model that Manabe published in 1975, the direct ancestor of today's climate models.

Hasselmann's problem, about ten years later, was different: how can a long-term climate trend be trusted when the short-term weather behind it is chaotic and noisy? He treated the fast, unpredictable weather as random noise acting on the slow-moving climate, borrowing the idea from Albert Einstein's description of Brownian motion, the random walk of pollen grains jostled by water molecules.

In this analogy, the chaotic weather plays the part of the water molecules, and the climate is the slowly drifting pollen grain.

Hasselmann then developed statistical methods to pull out specific "fingerprints", that is, characteristic patterns that natural causes such as volcanic eruptions and human causes such as carbon dioxide emissions each leave on the climate record, which has since been used to attribute the observed warming to human emissions.

Draw a jagged, rapidly zig-zagging line labelled "weather" running above and below a smooth, slowly rising line labelled "climate trend", with an arrow showing that the average of the fast zig-zags over time traces out the slow trend, similar to how a dog running randomly around a person still reveals the person's steady walking direction.

What did Giorgio Parisi discover about disordered systems?

Parisi's starting point was statistical mechanics, the branch of physics founded in the late nineteenth century by James C. Maxwell, Ludwig Boltzmann and J.

Willard Gibbs, which explains bulk properties such as temperature and pressure as the average behaviour of huge numbers of particles.

This works well for ordinary gases and liquids, but it struggled with spin glasses, where frustration between neighbouring magnetic atoms means there is no single obvious "best" arrangement, only many almost-equally-good ones.

Physicists in the 1970s tried to handle this with the replica trick, a mathematical method that processes many imagined copies, or replicas, of the same disordered system at once.

The early versions gave results that did not correspond to anything physically sensible. In 1979, Parisi found a way to use the replica trick properly:

1. Take many replicas of the disordered spin glass and compare how similar or different their frozen spin arrangements are to one another.
2. Instead of treating the replicas as either identical or completely independent, allow a whole hierarchy of overlaps between replicas, grouped within groups within groups.
3. Describe this nested structure mathematically, which revealed a hidden pattern inside what had looked like pure randomness.
4. Show that this structure predicts measurable physical properties of the spin glass, giving a theory that could later be tested and, after further work by other researchers, proven mathematically correct.

Parisi himself compared the frustration in a spin glass to the tangled loyalties in a Shakespearean tragedy, where some pairs of characters want to agree and others are set against each other, so the whole group can never fully settle into a stress-free arrangement.

Draw a few small magnets (spins) in a grid where neighbouring pairs want to point the same way or opposite ways in conflicting combinations, so no single arrangement satisfies every pair at once, illustrating the "frustration" that makes spin glasses hard to settle into one stable state.

The same mathematics turned out to describe many other frustrated systems: ordinary glass, granular materials such as sand, and, more broadly, problems in mathematics, biology, neuroscience and machine learning, anywhere that simple local rules produce a complicated collective outcome, such as a flock of starlings forming shifting patterns in the sky.

How did the discovery unfold?

The two strands recognised by the 2021 prize, climate physics and the theory of disordered systems, developed over roughly two centuries, converging in the award announced in 2021.

Why does it matter?

The climate half of the prize gave the world a scientifically solid basis for saying that the observed warming of about 1°C over the past 150 years is caused by human greenhouse gas emissions rather than by natural factors alone.

The committee noted that this year's discoveries show knowledge about the climate "rests on a solid scientific foundation, based on a rigorous analysis of observations," in the words of Thors Hans Hansson, chair of the Nobel Committee for Physics.

Manabe and Hasselmann's methods remain the backbone of the climate models used today to project future warming under different emission scenarios.

Parisi's half matters well beyond physics. His mathematics for handling frustration and disorder has since been applied to machine learning, and to understanding collective animal behaviour such as flocking, because all these situations involve many simple parts whose local conflicts produce a complex, structured whole.

Open questions remain in both fields: climate scientists continue refining models of clouds, oceans and ice sheets, while physicists still extend Parisi's methods to new disordered and frustrated systems.

How does this connect to what you study?

The greenhouse effect, carbon dioxide levels and global warming that sit at the heart of Manabe and Hasselmann's work also appear in school geography and environmental science lessons on climate change. The basic idea that certain gases absorb and re-emit infrared radiation, while others such as nitrogen and oxygen do not, links directly to chemistry lessons on molecular structure, energy absorption and the composition of the atmosphere.

The historical build-up of this science, from Joseph Fourier's early work on radiation balance through Svante Arrhenius's calculations to Manabe's computer models, mirrors how physics lessons often show a single scientific question being refined by successive researchers over many decades rather than solved all at once.

Parisi's work on disordered systems shares its mathematical language with the statistics and probability topics taught in school mathematics, since both deal with predicting average, large-scale behaviour from many individual random events, such as working out an average from repeated trials.

His idea that simple local rules among many interacting parts can produce complicated collective behaviour, as with a flock of birds forming shifting patterns, also connects to biology lessons on populations and group behaviour, where the actions of many individual organisms combine to produce patterns that no single organism controls on its own.

Quick facts for exams

The Nobel Prize in Physics 2021 was announced on 5 October 2021 by the Royal Swedish Academy of Sciences, carrying a prize amount of 10 million Swedish kronor.

It was awarded "for groundbreaking contributions to our understanding of complex physical systems," split so that Syukuro Manabe (Princeton University, USA) and Klaus Hasselmann (Max Planck Institute for Meteorology, Germany) shared one half for modelling Earth's climate, while Giorgio Parisi (Sapienza University of Rome, Italy) received the other half alone for discovering hidden order in disordered systems such as spin glasses.

Manabe and Hasselmann were both born in 1931, in Japan and Germany respectively, and Parisi was born in Italy in 1948.

Note: Source. The prize facts in this note are from the Nobel Prize's official site, nobelprize.org.

Glossary

• Complex system — a system made of many interacting parts whose combined behaviour is hard to predict, such as the climate or a disordered material.
• Chaos theory — the study of systems where tiny differences in starting conditions lead to very different outcomes over time, such as the weather.
• Butterfly effect — the idea that a very small change, such as a butterfly's wingbeat, can eventually lead to a large difference in a chaotic system.
• Greenhouse effect — the trapping of outgoing infrared heat by atmospheric gases, which keeps Earth's surface warmer than it would otherwise be.
• Feedback mechanism — a process where a change causes further changes that either amplify or reduce the original effect, such as warming increasing water vapour.
• Stochastic model — a mathematical model that deliberately includes randomness or chance as part of its description of a system.
• Brownian motion — the random, jittery movement of small particles caused by collisions with surrounding molecules, used by Einstein as a theoretical model.
• Fingerprint (climate science) — a characteristic pattern that a particular cause, natural or human, leaves on climate data, allowing scientists to identify its source.
• Spin glass — a metal alloy with randomly placed magnetic atoms whose spins cannot all settle into agreement, producing frustrated, puzzling magnetic behaviour.
• Frustration (physics) — a situation where the interacting parts of a system cannot all simultaneously satisfy their preferred arrangement.
• Replica trick — a mathematical method that analyses many copies of a disordered system together to work out its average properties.
• Statistical mechanics — the branch of physics that explains the bulk properties of matter, such as temperature, from the average behaviour of its particles.
• Keeling Curve — the long-running record of atmospheric carbon dioxide measurements begun at the Mauna Loa Observatory in 1958.

Common errors and misconceptions

• Misconception: The entire 2021 Physics prize was about climate change. Correct: Only one half went to Manabe and Hasselmann for climate modelling; the other half went to Parisi for disordered systems unrelated to climate.
• Misconception: Manabe and Hasselmann proved climate change is real for the first time. Correct: Earlier work by Arrhenius and Fourier had already proposed the underlying greenhouse mechanism; the laureates built the reliable physical models and statistical methods that confirmed and quantified it.
• Misconception: Because weather is chaotic, climate predictions must also be unreliable. Correct: Hasselmann showed that chaotic short-term weather can be treated as noise, allowing long-term climate trends to be modelled reliably.
• Misconception: Parisi's work only applies to magnets. Correct: His mathematics for frustrated, disordered systems has since been applied to glasses, granular materials, biology, neuroscience and machine learning.
• Misconception: Carbon dioxide is the most abundant greenhouse gas by volume in the atmosphere. Correct: Carbon dioxide makes up only about 0.04 per cent of the atmosphere by volume; nitrogen and oxygen together make up about 99 per cent.
• Misconception: The replica trick was Parisi's own invention from scratch. Correct: Other physicists had already been using the replica trick in the 1970s; Parisi's breakthrough in 1979 was finding how to use it correctly to solve the spin glass problem.
• Misconception: All three laureates worked together as a team. Correct: Manabe and Hasselmann worked on related climate problems about a decade apart, while Parisi worked independently on a different class of physical systems.

Exam-style questions with model answers

Q1. For what overall citation was the Nobel Prize in Physics 2021 awarded? [2 marks]

1. It was awarded "for groundbreaking contributions to our understanding of complex physical systems," recognising work on the climate and on disordered materials.

Q2. Name the three laureates of the Nobel Prize in Physics 2021 and their share of the prize. [2 marks]

1. Syukuro Manabe received one quarter, Klaus Hasselmann received one quarter, and Giorgio Parisi received one half of the prize.

Q3. Explain, in brief, how Syukuro Manabe's climate model worked. [4 marks]

1. Manabe reduced the atmosphere to a one-dimensional vertical column about 40 kilometres high to make the calculations manageable with the computers available in the 1960s.
2. He added the vertical transport of air by convection and the latent heat released when water vapour condenses, alongside the radiation balance used in earlier models.
3. By varying the level of each atmospheric gas, he found that doubling carbon dioxide raised global surface temperature by over 2°C, while oxygen and nitrogen had negligible effect.
4. The resulting warming pattern, with the lower atmosphere warming and the upper atmosphere cooling, confirmed carbon dioxide, rather than solar changes, as the cause.

Q4. What problem did Klaus Hasselmann solve, and how? [4 marks]

1. Hasselmann addressed why long-term climate predictions could be reliable even though short-term weather is chaotic and unpredictable.
2. He treated the fast, random weather fluctuations as noise acting on the slower-moving climate, using an analogy with Einstein's theory of Brownian motion.
3. This stochastic approach showed that rapid, chaotic weather changes could still produce slow, predictable variations in the climate.
4. He also developed fingerprint methods that separate out the specific signals left by natural causes and by human carbon dioxide emissions in temperature records.

Q5. What is a spin glass, and why is it described as "frustrated"? [3 marks]

1. A spin glass is a metal alloy, such as iron atoms randomly mixed into a grid of copper atoms, where each iron atom behaves like a small magnet, or spin.
2. Neighbouring spins are affected by each other, with some pairs wanting to align and others wanting to oppose each other.
3. Because these preferences conflict, no single arrangement can satisfy every pair at once, which is why the system is called frustrated.

Q6. Describe Giorgio Parisi's contribution to the theory of disordered systems and discuss its wider impact. [5 marks]

1. In 1979, Parisi found how to properly use the replica trick, a method that analyses many copies of a disordered system together, to solve the long-standing spin glass problem.
2. He discovered a hidden, nested hierarchical structure within the replicas, and described this structure mathematically, revealing order inside what had looked like pure randomness.
3. It took many years for other researchers to prove his solution mathematically correct, after which his method became a cornerstone of the theory of complex systems.
4. The same mathematics was later applied to ordinary glass, granular materials such as sand, and, more broadly, to problems in mathematics, biology, neuroscience and machine learning.
5. Parisi's work showed that very different frustrated systems, from spin glasses to flocks of starlings, can share the same underlying mathematical description of how simple local rules produce complex collective behaviour.

Q7. Why does the greenhouse effect make Earth's temperature higher than it would otherwise be? [3 marks]

1. Sunlight reaches Earth's surface and is converted into outgoing infrared radiation, sometimes called "dark heat."
2. Greenhouse gases such as carbon dioxide, methane and water vapour absorb this outgoing radiation and re-emit it, warming the surrounding air.
3. Without this trapping effect, the surface would be far colder, since the atmosphere would simply let the outgoing heat escape into space.

Q8. Discuss why the committee divided the 2021 Physics prize into two separate halves rather than giving it for a single discovery. [4 marks]

1. The prize recognised two distinct contributions to understanding complex physical systems, systems made of many interacting parts whose combined behaviour is hard to predict.
2. Manabe and Hasselmann's work concerned Earth's climate specifically, building physical and statistical models that made long-term climate prediction scientifically reliable.
3. Parisi's work concerned a different class of systems, disordered materials such as spin glasses, and used different mathematical tools, the replica trick, rather than atmospheric physics.
4. Because the two contributions addressed different physical systems with different methods, even though both dealt with randomness and disorder, the Royal Swedish Academy of Sciences split the award, giving one half jointly to the climate modellers and the other half entirely to Parisi.

Key takeaways

• The Nobel Prize in Physics 2021 honoured work on complex physical systems, split between climate modelling and disordered materials.
• Manabe and Hasselmann shared one half of the prize for physically modelling Earth's climate and reliably predicting global warming.
• Parisi received the other half alone for discovering hidden patterns in disordered systems such as spin glasses.
• Manabe's one-dimensional atmospheric model in the 1960s showed carbon dioxide, not solar changes, drives surface warming.
• Hasselmann treated chaotic weather as noise to make long-term climate prediction scientifically reliable, and devised fingerprint methods for human influence.
• Parisi's 1979 solution to the spin glass problem, using the replica trick, uncovered a hidden hierarchical structure inside apparent randomness.
• Parisi's mathematics now informs fields well beyond physics, including biology, neuroscience and machine learning.
• The prize carries 10 million Swedish kronor and was announced on 5 October 2021.

Test yourself

Who shared Hasselmann's half of the 2021 Physics prize?

Syukuro Manabe shared the climate-modelling half of the prize jointly with Klaus Hasselmann.

Where was Giorgio Parisi affiliated at the time of the award?

Giorgio Parisi was a professor at Sapienza University of Rome in Italy when he received the prize.

What trick did Parisi use to solve the spin glass problem?

Parisi used the replica trick, analysing many copies of the disordered system together to find its hidden structure.

What analogy did Hasselmann use to link weather and climate?

He compared chaotic weather to Einstein's Brownian motion, treating weather as noise driving the slower climate signal.

What did Manabe's model show about doubling atmospheric carbon dioxide?

Manabe's model showed that doubling carbon dioxide raised global surface temperature by over 2°C.

What does "frustration" mean for a spin glass?

Frustration means neighbouring magnetic spins have conflicting preferences, so no arrangement can satisfy every pair at once.

When was the Nobel Prize in Physics 2021 announced?

The prize was announced on 5 October 2021 by the Royal Swedish Academy of Sciences.