Colloquium on 2021 Nobel Prize in Physics

 Every year the UQ Physics Department has a colloquium where someone describes the science behind the latest Nobel Prize. This year I am going to talk about Parisi and the spin glass problem. My colleague Henry Nourse will talk about the climate modelling part.

In preparation, I have found the book, Spin Glasses and Complexity by Daniel L. Stein and Charles M. Newman, very helpful. It is at the level of a colloquium and has a nice chapter on applications to other areas of science (e.g. proteins, simulated annealing, optimisation, computer science, ...) It enabled me to finally "understand" the background and significance of Hopfield's famous paper from 1982, "Neural networks and physical systems with emergent collective computational abilities".

Thinking about replica symmetry breaking has brought back memories of when I was a graduate student at Princeton. When I started Anderson was thinking about spin glasses a lot and had people working on it. I heard lots of talks about spin glasses, replica symmetry breaking, travelling salesmen, ultrametricity, ... Even David Gross gave a colloquium about work he did on spin glasses, with a very warm introduction by Phil. ["I introduce David Gross the condensed matter theorist"] However, once the cuprates happened at the end of 1986, Anderson seemed to largely drop the spin-glass work. Except for Dan Stein, everyone started working on cuprates. In hindsight, I wonder if that was a mistake. In particular, it might have been better for many of his students if they had worked on complexity rather than cuprates.

Next week I will post a draft of my slides. In the meantime, two questions for readers:

1. What are some specific questions you might like answered in such a colloquium?

2. What are some specific resources you may have come across about this year's prize that you found helpful or interesting?

Here are the slides.

Management is not leadership. II

 Previously, I have argued that being in management is neither a necessary nor a sufficient condition for showing leadership. I have also discussed how some articles about management, such as in the Harvard Business Review, can be helpful in academic contexts. This is in spite of the fact that I detest the idea that the university is a "business".

Here I bring the two points together. There is a nice short article in the HBR,Three Differences Between Managers and Leaders by Vineet Nayar

Counting value vs Creating value. Only managers count value; some even reduce value by disabling those who add value.

Circles of influence vs Circles of power. Managers have subordinates and leaders have followers. 

Leading people vs Managing work. Management consists of controlling a group or a set of entities to accomplish a goal. [Leaders]... influence, motivate, and enable others to contribute toward organizational success. 

Why are superfluids creepy?

 A signature effect associated with superfluidity in liquid helium is that it can climb up the walls of a container and empty the container. This is seen in the video below (beginning at 1:10).

But what is the physics behind this? 

Why is this a signature of superfluidity?

The schematic below is helpful. [It is figure 1.8 in Superfluidity and Superconductivity by Tilley and Tilley.]

We need to distinguish between which parts of the underlying physics occur for all fluids and which only occur for a superfluid.

1. For any liquid in thermodynamic equilibrium inside a container there is some vapour present. Some of this vapour condenses onto the surface of the container, forming a thin film of liquid on the surface. The surface of the liquid is actually not completely flat but curves upwards at the edge of the container surface. An example of this is a concave meniscus that one sees inside a small tube.

2. For a normal fluid the surface film is relatively thin and is pinned to the container surface by the viscosity of the fluid.

3. In superfluid helium the film is thick enough that the superfluid component of the fluid can flow freely. The film also extends to the top of the container walls.

Thus, the superfluid forms a continuous film that extends up and over the container walls. 

4. Superfluid in the film can flow freely if there is a driving force. The difference in gravitational potential energy between the surfaces of the liquid inside and outside the container provides such a driving force. The physics of this is identical to that of a regular siphon. It is just that in the case of superfluid helium the "tube" is the surface film and that due to superfluidity this film can flow.

And so, that is why superfluids are creepy.

The biochemical basis of mental health basics

 Yesterday the UQ Brain Institute had an excellent webinar Brain Health for Mental Health. Four researchers discussed the scientific basis for some simple strategies to reduce the likelihood of mental illness and/or to aid its treatment. These include

eat well

exercise regularly

sleep well

reduce screen time

drink less caffeine

minimise international travel (because of the associated jet lag).

I was fascinated to see the biological and biochemical basis for these strategies. I try to implement them myself and often emphasise the importance of these basic disciplines to others.

Some of the science is fascinating in itself. Did you know you can study sleep in fruit flies?

The webinar also provides a nice example of a public engagement activity. Rather than having one person give a long talk, four different researchers speak, and each for only five minutes with about five slides each. Each talk is followed by a question from the chair. Then at the end there are questions from the live online audience.

2021 Nobel Prize in Physics: from spin glasses to complexity theory

I was delighted to hear of the award of the Nobel Prize in Physics for 2021. The committee continues to surprise us. I did not make any predictions this year, because I had nothing new to predict. I am still surprised that experimental tests of Bell inequalities (Aspect, Clauser, Zeilinger) have still not got a prize. Maybe next year.

Here I will just write about the award to Giorgio Parisi “for the discovery of the interplay of disorder and fluctuations in physical systems from atomic to planetary scales” as it involves condensed matter theory, beginning with spin glasses, and like many things with Phil Anderson!

The popular science background and the scientific background to the prize are worth reading, as always. It notes that in a Physics Today column Anderson wrote in 1988,

“The history of spin glass may be the best example I know of the dictum that a real scientific mystery is worth pursuing to the ends of the Earth for its own sake, independently of any obvious practical importance or intellectual glamour.” 

This was in the first of a series of seven Reference Frame columns he wrote on spin glasses. The fifth column described the work of Parisi.

Here I will describe the basic ideas, particularly as they show that sometimes obscure basic science questions, very abstract ideas and mathematical formulations can be useful for very practical scientific questions, across a wide range of disciplines.

A spin glass is a distinct state of matter. This means, that in terms of the Landau paradigm, there must be an order parameter and an associated broken symmetry. What are they? Parisi found the answers.

First, as one usually does in theoretical condensed matter, one needs to write down a minimal model Hamiltonian that is complex enough to capture the essential physics but is simple enough to be amenable to analytical and/or computational analysis. 

Sam Edwards and Anderson proposed the following model for a spin glass, and Ising model where the spins are on a regular lattice but the interaction between any pair of spins, J_ik, is a random Gaussian variable with zero mean and non-zero variance.

This means that the interspin interactions are equally likely to be ferromagnetic or antiferromagnetic, leading to significant frustration.

To solve such a model one needs to calculate the partition function Z for each realisation of the J's (disorder), calculate F=- T ln Z, and average over all the configurations of disorder. 

Averaging Z over disorder is just a Gaussian integral, but averaging ln Z is analytically intractable.

Anderson's physical intuition was combined with the mathematical trickery of Edwards, that he had cultivated with his earlier work on quantum field theory and soft matter.

The replica trick is based on an identity that one learns in introductory calculus.

One considers not one system but rather n identical copies (replicas) of the physical system, calculates the average of the partition function for this fictional n-system, and then treats n as a continuous analytical variable and takes the limit that n goes to zero in the formula above. Wow, that is abstract! But, it is tractable.

Personal aside: more than twenty years ago I learned and used the replica trick because (like supersymmetry) as it provides a powerful mathematical tool to treat disorder exactly in one-dimensional models. But, the spin-glass case is much richer and more subtle.

Strange things happen for the spin glass. Soon after Edwards and Anderson's work, Thouless, Anderson, Palmer, and others made the rather puzzling discovery that not all the replicas were the same below the temperature associated with transition to the spin-glass state. The replica symmetry was broken in the spin-glass state.

Parisi proposed the order parameter below for this broken symmetry state. i denotes a lattice site, and the indices alpha and beta denote replicas. When alpha and beta have different values, the order parameter only becomes non-zero when the replicas are different.

Parisi, Toulouse, Mezard, and others then showed that there is a hierarchical structure associated with the order parameter leading to the concept of ultrametricity which can be associated with the rugged energy landscape of not just the spin-glass problem, but also optimisation problems, simulated annealing, protein folding, neural networks, ...

A nice overview that puts the theory of spin glasses in a much broader scientific context is Physics and Complexity by David Sherrington.

On Doug Natelson's blog, nanoscale views, there is a nice discussion in the comments about Parisi's Nobel and the subtle issue of the connections between separation of time scales and ultrametricity, and the connections (or not) between Parisi and climate science.

What do we really understand about cuprate superconductors?

 At a recent meeting of the condensed matter theory group at UQ we watched the first half of a Harvard (online) seminar that Steve Kivelson gave (at the end of 2020), What do we know about the essential physics of high temperature superconductivity after one third of a century?

As a springboard he takes Phil Anderson's final posting of the arXiv, Last Word's on the Cuprates, from the end of 2016. He was 93 years old then!

Kivelson considers that there are two things we really understand about the cuprates. The first, is that the d-wave superconductivity is intimately connected with the antiferromagnetism of the undoped materials.

The second, is that Tc, the superconducting transition temperature, is determined by thermal disordering of the phase of the order parameter for the superconducting state. This is in contrast to conventional superconductors, where Tc is determined by the amplitude of the order parameter vanishing. 

Kivelson's argument for the first point is based on nice work done a decade ago with Sri Raghu and Doug Scalapino, and that led to other work I have blogged about. It should be stressed that this work is a weak-coupling renormalisation group treatment and so the question remains as to whether the phase diagram for weak-coupling is adiabatically connected to that for strong coupling, which is the regime of the actual cuprate materials. In different works, as U/t increases from very small values to large values there are no phase transitions. Cluster Dynamical Mean-Field Theory (DMFT) studies give some confidence that this is the case. However, not everyone will be convinced by that.

The talk is worth watching, even if at times it gets a bit too technical. It is very important that we have such honest and open reflections about how much progress is (not) being made in a field. I largely agree with Kivelson, but do find the lack of progress rather discouraging and cannot see that this will be inspiring bright young graduate students to enter the field or for funding agencies to put more money into it.