Des Johnston
School of Mathematical and Computer Sciences
Maxwell Institute for Mathematical Sciences
Heriot-Watt University
Riccarton, Edinburgh EH14 4AS

Email: D.A.Johnston -at-
Office: CMS.04
Phone: +44 (0)131 4513255
Fax: +44 (0)131 4513249
Anti-Social Networks: Facebook, Twitter, Linkedin

e-prints: ArXiv, PURE
Bibliometrics: Google Scholar, Scopus, Mendeley, INSPIRE, ORCID, ResearchGate, Publons, ReseacherID

History: Maths department history

Once upon a time there was a nicer looking page but then all the style sheets got broken, so this is just an ugly page of lists on a pale grey background. However, you are a click away from a (slightly) better typeset Academic CV.

2017 vintage pic

A better likeness?

(Fairly) Current Research Interests: 3D Plaquette Ising Model, Fractons etc

    I keep circling back to the 3D Plaquette Ising Model, having first run across it many moons ago when we discovered that it had a first order phase transition (which was bad news at the time, since we were looking for continuum limits). Much more recently work with Marco Mueller and Wolfhard Janke of Leipzig University found non-standard scaling behaviour at the first order transition since the the low temperature phase is highly degenerate as the result of a subsystem symmetry, intermediate between a global and a local (gauge) symmetry.

    Such subsystem symmetries have recently been implicated in fractonic models, in which quasiparticle excitations display restricted (or even zero) mobility. Indeed, gauging the subsystem symmetry in the quantum 3D Plaquette Ising Model gives rise to a canonical fractonic model, the X-cube model, in much the same way as gauging the global symmetry of the standard quantum 2D Ising model gives rise to the toric code.

(Fairly) Recent Papers

Coauthors from Heriot-Watt PURE

Sofa Seminar Videos - Slides+Narration

Recorded during the COVID-19 lockdown, largely to experiment with recording on various platforms.

Macos: cmd-shift-5 does the trick, gives a .mov which can be transcoded to mp4.
Linux/Chrome OS: Screencastify Chrome extension (you pay for some features), records to webm and can export to mp4. I had sound issues with other possible solutions in Linux, YMMV.

(Fairly) Recent Research Talks/Posters

1984 vintage pic

PhD Era Research Interests: Nielsen Identities etc

The framework for understanding particle physics over the past decades has been that of gauge symmetry. The Standard Model in particle physics was constructed by bolting together gauge theories for electromagnetism and the Strong and Weak interactions, with the essential additional ingredient of the Higgs Boson to generate mass while preserving the gauge symmetries. The mechanism for such mass generation is spontaneous symmetry breaking, where the vacuum solutions of the theory have less symmetry than the Lagrangian describing the theory.

In order to perform perturbative calculations in such theories it is necessary (or at least convenient) to "fix the gauge", which leads to results for physical quantities, such as the mass of particles, which apparently depend on unphysical parameters introduced in the gauge fixing. My job in my thesis was to show with explicit calculations in a particular model that such dependence was illusory and that, in fact, all was well. The work made use of the so-called Nielsen Identities to demonstrate the gauge-independence of physical quantities.

Some Associated Published Papers

What a preprint (my first...) used to look like in those prehistoric days before TeX (1984): Nielsen Identities in the 't Hooft Gauge

What a thesis (my only...) used to look like in those prehistoric days before TeX (1986): Gauge Properties and Convexity of the Effective Potential

Heriot-Watt Lectures

Heriot-Watt maths courses:
Maths Masterclass (schools talk):

AIMS Lectures

AIMS Ghana course:
AIMS South Africa course:
AIMS Senegal course: