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

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






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

History: Maths department history


Peering into the sun at AIMS-Senegal 2017





Word cloud of research interests from scimeter.org using ArXiv


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.



(Fairly) Current Research Interests: First Order Phase Transitions

    To some extent first-order phase transitions, that is transitions where there are discontinuities (latent heat and jumps in density or volume) have been the poor cousins of continuous transitions (where there are no such jumps) when it comes to numerical investigations, in spite of their prevalence in nature. There are various reasons for this - they are harder to simulate, for instance, and there appear to be fewer distinct quantities to measure for the first order transitions compared with continuous transitions.

    Recent research work along with Marco Mueller and Wolfhard Janke of Leipzig University has concentrated on several aspects of such first order transitions, in particular non-standard scaling behaviour at first order transitions when the low temperature phases are highly degenerate. As luck would have it, an old favorite - the Gonihedric Ising model - provides an example of this.

    Collaborations with colleagues at Coventry University and a visitor from Sri Lanka, R.P.K.C.M. Ranasinghe, have also investigated the phase transitions of Potts models with so-called invisible states, which display unexpected first order transitions, clarifying why they occur.

(Fairly) Recent Papers




(Fairly) Recent Research Talks/Posters




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.

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

Some Associated Published Papers





Heriot-Watt Lectures


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

AIMS Lectures


AIMS Ghana course:
AIMS South Africa course:
AIMS Senegal course:
  • March/April 2017, 2018: Quantum Mechanics and Quantum Computing