Editorial Feature

The Physics of Disordered Materials and Random Processes

The 2021 Nobel Prize in Physics recognized the work of a man who saw the frustration in complex and disordered systems and set about understanding it.

complex systems, physics, nobel prize, nobel, spin glasses, disordered systems

Image Credit: agsandrew/Shutterstock.com

The 2021 Nobel Prize in Physics has been handed out to US-Japanese scientist Syukuro Manabe, Klaus Hasselmann of Germany, and Giorgio Parisi of Italy. The former researchers share half of the prize, including the financial award of $1.1-million, for their work with climate models. 

Parisi, 73, was awarded half of the prize for his work on the interplay between disorder and fluctuations in physical systems. The Nobel Committee says the prize motivation for award to the Sapienza University of Rome, Rome, Italy, researcher as: “for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales.”

Perhaps the most extraordinary thing about Parisi’s work is just how wide-ranging his mathematical solution has proved to be.

Complex Systems Connecting Climate Ecosystems, Financial Systems, and Biological Processes

Before Parisi’s work, scientists would struggle to suggest a link between fluctuating stock markets and the behaviour of flocks of starlings, not to mention a set of universal rules to govern them.

Such systems look completely unpredictable and random, but Parasi’s work revealed a method of modelling them.

One of the key characteristics of complex systems that separates them from other systems is the fact that they are not a collection of identical particles or other bodies that are interacting in predictable ways. In complex systems, differing elements interact in a variety of seemingly unpredictable ways, especially when they are exposed to external influences.

Understanding and modelling these complex systems is an important stepping stone to describing disordered systems — different pairs of elements experience different, potentially conflicting forces that can lead the elements to become “frustrated.” 

The award specifically honours Parisi’s work with one such frustrated system, so-called “spin glasses.” 

Solving this problem has led to a solution that has proved to be applicable in the study of a wide range of complex physical systems, ranging from the cosmological to the quantum.

What Are Spin Glasses?

Spin glasses are crystalline materials into which a few magnetic atoms are introduced. In these disordered magnetic systems, the competition between exchange interactions does not lead to a long-range ordering of magnetic moments. Instead, it results in the distribution being “frozen in.”

This results in a situation in which the magnetic atoms align themselves in the opposite way with respect to their neighbours. So, if one atom points up, a second points down. However, this means a third atom would not be able to align itself opposite its two neighbours.

The result is a frustrated system — a system in which two or more interaction terms are conflicting with each other — with a configuration that was difficult for physicists to calculate.

"This work holds up a light for other scientists going forward."

Video Credit: Nobel Prize/Youtube.com

Parisi became interested in spin glasses due to his work in particle physics. The Italian researcher was interested in the use of replicas to understand spin glasses. This is known as the “replica trick” and uses the averages obtained by physical replicas of a system to understand that system.

However, he found that when this “replica trick” was allied to spin glasses, unphysical results were obtained. This told Parisi that spin glasses must have an infinite number of possible states. In response to this revelation, Parisi modified the replica trick by assigning it a new parameter that described the resemblance between two replica systems. 

The mathematical method developed by Parisi would find applications in a variety of disordered systems beyond spin glasses, going on to be pitted against several long-standing problems in other physics fields.

Parisi Relieves Frustration and Disorder

Paolo Barucca is a lecturer at the Department of Computer Science, University College London; he studied for his masters under Parisi. He gave an analogy of Parisi’s work solving frustrated systems to The Conversation:

He suggests thinking of frustrated systems as a party; gathered are Alice, Bob and Charlie. The frustration arises from the fact Alice wants to talk to Bob, Bob wants to talk to Charlie, but Charlie does not want to speak with Alice.

What Parisi suggested is that frustrated complex systems can “remember” past trajectories over time and sometimes get trapped in sub-optimal states. In Barucca’s party analogy, this is equivalent to Alice, Bob, Charlie, and other guests irregularly changing conversational groups and partners, hoping to find the best group of people to chat with — yet potentially never finding it. 

This is the sub-optimal state complex systems can get stuck in.

The replica trick used by Parisi replicates the party over and over again many times. How the social event proceeds and how its guests mingle to find the optimal arrangement can be found in the patterns that emerge from the replicas.

This leads to a framework applicable to everything from supercooled liquids, to flocking birds, to climate systems — the latter of which connects Parisi to the researchers with which he shares the 2021 Nobel in Physics.

Barucca was not surprised his former tutor received a Nobel, but was pleasantly shocked that it was for his work with complex systems, which may not on face value seem as exciting as the discovery of the first exoplanet or black hole research that scooped part of the physics Nobel prize in 2019 and 2020, respectively.

Barucca believes this may be an important step to bringing more attention to the field of complex and disordered systems. 

References and Further Reading

Giorgio Parisi, The Nobel Prize

Schweizer. J., [2006], Polarized Neutrons and Polarization Analysis, Polarized Neutrons and Polarization Analysis. 

Barucca. P., [2021], The Conversation.

Disclaimer: The views expressed here are those of the author expressed in their private capacity and do not necessarily represent the views of AZoM.com Limited T/A AZoNetwork the owner and operator of this website. This disclaimer forms part of the Terms and conditions of use of this website.

Robert Lea

Written by

Robert Lea

Robert is a Freelance Science Journalist with a STEM BSc. He specializes in Physics, Space, Astronomy, Astrophysics, Quantum Physics, and SciComm. Robert is an ABSW member, and aWCSJ 2019 and IOP Fellow.


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