Physics 569: Emergent States of Matter

Spring 2021

Instructor: Nigel Goldenfeld

Time: 2.00-3.20pm, Mondays and Wednesdays
Place: Online

Nigel's office hour will be Monday at 5pm online

Course gradebook for the full course.

Lecture notes for the course are available online. A list of typos can be found here; please add to it if you find any.



Thomas Johnson ( will have office hour online Wednesdays at 5.15pm.

Manthos Karydas ( will have office hour online Tuesdays at 5pm

2021 Spring Term Essays are here.

Other than that ... Nothing to see here. Move along or watch a movie.

Handouts and Assignments

Course details

Revision of 2nd Quantisation

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

Homework 8

Tentative syllabus.

  1. Emergent states and long-range order
    Introduction to emergent states; long-range order; continuous symmetries
  2. Off-diagonal long-range order
    Bose-Einstein condensation; topological excitations; quasi-particles
  3. General theory of spontaneous symmetry breaking
    Goldstone's theorem; response functions; excitations; emergent properties; Landau theory; generalized elasticity theory
  4. Pairing in superconductors and nuclear matter
    Ginzburg-Landau theory; BCS theory; QCD
  5. Liquid crystals
    Nematics and smectics; analogue with superconductivity
  6. Emergence in complex biological systems
    Networks and self-organisation
  7. Emergent states far from equilibrium
    Rayleigh-Benard convection; bifurcations; Landau theory and generalized elasticity theory far from equilibrium

Emergent states of matter movie page

Superfluid flow phenomena can be visualized with some ingenuity, and I have assembled some resources related to superfluidity on the emergent states of matter movie page. In the future, I may add other material to this page.

Recommended books

I have not yet written a textbook for this course which covers all the material in the way I teach it. However, past students in this course have found that the books below are useful supplements to my class notes.

(A) General references on spontaneous symmetry breaking, Landau theory and generalized elasticity theory.

P. Chaikin and T. Lubensky. Principles of Condensed Matter Physics.

N. Goldenfeld. Lectures on Phase Transitions and the Renormalization Group.

L.H. Ryder. Quantum Field Theory. There is no quantum field theory per se in the course, but some students liked the discussion of symmetry breaking in this book.

A. Altland and Ben Simons. Condensed Matter Field Theory. This is an advanced book, but one of the best to learn about the modern approach to condensed matter theory, with many-body theory done by functional integral techniques, and a clear and readable presentation of many technical issues.

Mehran Kardar. Statistical Physics of Fields. A clear and well-written introduction to modern ways to deal with collective phenomena in condensed matter physics.

(B) Off-diagonal long-range order and condensates

J. Annett. Superconductivity, Superfluids and Condensates.

C.J. Pethick and H. Smith. Bose-Einstein Condensation in Dilute Gases

(C) Superconductivity

M. Tinkham. Introduction to Superconductivity.

(D) Liquid Crystals

P.G. de Gennes. The Physics of Liquid Crystals.

(E) Quantum Hall Effects

M. Stone. The Quantum Hall Effect.

(F) Biological emergence

S. Strogatz. Sync

C. R. Woese. On the evolution of cells, Proc. Natl. Acad. Sci. USA 99, 8742-7 (2002).

(G) Pattern Formation

M. Cross and P. Hohenberg. Pattern Formation Outside of Equilibrium, Reviews of Modern Physics 65, 851-1112 (1993).

Complexity and emergent phenomena are very much frontier topics across disciplines of science. As an example, here is a report recently issued by the US Department of Energy on the importance of this topic.

Experimental Data


Here is a set of real experimental data on the penetration depth of the high temperature superconductor YBCO, which were published in S. Kamal, D. Bonn, N. D. Goldenfeld, Hirschfeld, R. Liang and W. N. Hardy. Penetration depth measurements of 3D XY critical behaviour in YBa2Cu3O6.95 crystals. Phys. Rev. Lett. 73, 1845-1848 (1994).

Term essay archive

2021 Spring Term Essays are here.

2018 SpringTerm Essays are here.

2012 Fall Term Essays are here

2011 Fall Term Essays are here

2010 Fall Term Essays are here

2009 Fall Term Essays are here

2008 Fall Term Essays are here

2007 Fall Term Essays are here

2006 Fall Term Essays are here

2006 Spring Term Essays are here

2004 Fall Term essays are here.

2004 Spring Term essays are here.

2002 Term essays are here.


Term Paper Instructions

Instead of a final exam, this course will have a term paper assignment. The subject matter can be any topic in physics which is related to Emergent States of Matter in some sense.  Since many interesting phenomena are a manifestation of emergence, you have unusual latitude in your choice of topic.  It need not be restricted to condensed matter but can cover the many recent and exciting developments in other areas of science, including, but not limited, to: high energy physics, cosmology, even biology.   I hope many of you will chose topics in these non-condensed matter areas.

Your essay should not duplicate an essay that you have written for another course, nor should it duplicate your research work. The purpose is to give you something fresh to write about, related to the topic of the course.

I can provide you with a guide to the literature for many topics if you come and ask me. However, I really don't want to do this. Part of this assignment is to give you an opportunity to develop the skills in doing a literature survey and digging up information from the library.  Other important components of this assignment are that you demonstrate good taste, curiosity and ambition in your choice of subject, and that you are capable of distilling the most important and essential details from very technical papers.

Some hints: look at the back of the current Reviews of Modern Physics where you will find a listing of topics that have been reviewed in the last ten years or so. These are always a good starting point. Similarly for journals such as Advances in Physics and Reports of Progress in Physics. Use internet keyword searches on archives and search engines such as Google.

Don't be restricted by the topics that we addressed in class. We didn't have time to cover the huge variety of emergent states of matter that arise in the real world. Here is a partial list of subject areas to prompt your thinking:

Exotic superfluidity

Superfluid phenomena in Helium 3
Superfluid phenomena in neutron stars
Superfluid phenomena in nuclei

Exotic superconductivity

Heavy fermion superconductors
Unconventional pairing states in cuprate superconductors
Unconventional pairing states in non-cuprate superconductors
Fluctuation effects in superconductors
Vortex liquids, glasses and other aspects of the magnetic phase diagram of the cuprates

Liquid crystals

Analogies between liquid crystals and superconductors
Smectic phases in liquid crystals
Dynamics of topological defects in liquid crystals
Phase transition kinetics in liquid crystals
Blue phases

Emergent states of matter

Ordered phases in optical lattices (superfluid, Mott insulators, ...)
Quantum hall states of rapidly rotating BECs
Magnetic states of condensed matter (ferromagnets, antiferromagnets, spin glass, ...)
Disordered states of matter (Griffiths phases, random field Ising models, localization, ...)

High energy physics

Phases of quantum chromodynamics
Recent experimental puzzles from RHIC
Quark-gluon plasma and its dynamics


The electroweak phase transition in the early universe and its consequences
Cosmological manifestations of strings and other topological defects
Space-time as an emergent phenomenon
Phase transitions and inflationary cosmology

Nonequilibrium systems

Collective behaviour in animals (herding, flocking, schooling, ...)
Traffic flow (shocks, phase diagram, pedestrians ...)
Reaction-diffusion patterns
Convection effects in fluids
Emergence of network properties (WWW, metabolic networks, ...)
Synchronisation of coupled oscillators

Detailed Directions

The purpose of your essay is to explain why the problem is interesting, what has been done, and what are the conclusions. Don't go into unnecessary technical details. The amount that you personally chose to work through the technical details is up to you; my goal is that you understand the broad issues. Hopefully you will find your topic sufficiently interesting that you will wish to delve deeper (and perhaps even think for yourself about the subject).  You should imagine that you are writing the paper for a reader who is like you were before you started thinking about your topic.  Every essay must include some sort of discussion of experiment or observations: these can either be the focus of the essay, or at least must be mentioned specifically with regard to how they demonstrate, provide counter-examples to, or otherwise inform theory.  Essays which are purely theoretical will receive a relatively lower grade than others.  More detailed suggestions about format are given below.

The final exam/paper is due by 10pm Wednesday, May 12 2021. No excuses for lateness will be accepted unless there are extenuating circumstances or previous arrangements have been made, in accord with University regulations. It should be no more than 12 pages long, single spaced 12 point font, including figures and references (include some up-to-date review articles, and try to limit the references to around 10 or so). I will not read more than 12 pages of an essay.  Essays are graded for effort, so if it is significantly shorter than 12 pages, it is likely that you will lose credit also. You have been warned! In addition to the 12 pages of the essay, there should be a cover page, which will consist of the following (a) Title, (b) author's name, (c) abstract.

Your essay must be written in an electronic format, including the figures, if any.  Ultimately, all essays will be posted on the WWW. The format for submission will ONLY be an Acrobat PDF file.

Submission instructions:

(A) Write your essay in TeX, Word, whatever, ... and then convert it to a PDF file. There are plenty of free tools to do that.

(B) Name your essay according to the following scheme

<Your last name>.pdf

(Example:    goldenfeld.pdf)

(C) Email to Nigel Goldenfeld <>

Make the subject heading of your email

569 ESM   <Your last name>.pdf

and have in the body of the email your name, the title and a brief  abstract of your essay.





Subject: 569 ESM  smith.pdf


Author: Freda Smith

Title: Critical dynamics of the superconducting transition


This essay describes the observations, computer simulations, and analytic theory of critical fluctuation contributions to the electrical and thermal conductivity near the superconducting transition of the high temperature superconductors YBCO and BSCCO.



Your paper should have approximately the following structure, but feel free to modify it to fit your chosen topic.  Here are some suggestions for the sorts of questions your paper should address to make it most useful to the reader.  As you will see, the purpose is not to focus too much on technical details.

Introduction and Background:

What hypotheses are being tested in this paper?

What information induced the authors to perform the experiments/theory?

What new methods or insights brought to bear on the problem?

Why did you chose to write about this topic? 

Why is this interesting or important?


What are the critical methods of the paper?

What enabling technologies are used?

What are the weaknesses of the methods used?

Are there other or better approaches that could be used?

Results and Discussion

What are the primary conclusions of the paper?

Did the authors prove their hypotheses?

What novel information or directions come from this work?

What control experiments were performed? (If appropriate)

What assumptions still remain in the work?

How could these assumptions be tested?

What other explanations for the observations are still possible?

What would you do next to advance this field?

Term essays from an earlier version of this course when it was on Liquid Helium and Superconductivity only

Miscellaneous Information

Nigel Goldenfeld

Telephone: (217)-333-8027

Office: 3113 ESB
Office hour: Mon 4pm-5pm or by appointment
Nigel Goldenfeld's Home Page

Updated: Jan 16 2018