Critical Phenomena and Field Theory

John Cardy

The use of field theoretic methods to study problems in critical phenomena has a long history, dating back to the 1970's. Field theory provides a natural framework incorporating ideas of scaling and the renormalisation group which explain much of the phenomenology of critical phenomena, as well as providing an approximate calculational scheme. In the 1980's this was supplemented by the powerful methods of conformal and integrable field theory which give exact information on many classical systems in two dimensions (and one-dimensional quantum systems).

I have for some time been involved in the development of this theory as applied to quenched random systems (for example, random magnets and disordered electronic systems) as well as to 'geometric' critical behaviour such as percolation and self-avoiding walks, which model polymers. A new development is this area is the description of the random curves which arise in these systems using stochastic Loewner evolution (SLE). Much of the this work is fairly mathematical, but the aim is always to derive results of physical significance, which can be tested against experiment or numerical simulation.

Another aspect of my work in the 1990s was the application of systematic field-theoretic renormalisation group methods to non-equilibrium critical behaviour, particularly in reaction-diffusion systems. I also collaborated on applications in biology.

In the 2000s I became interested in the computation of entropy as a measure of quantum entanglement in extended systems. The time-dependence of this following the preparation of the system in a general state led to a new field of research for which I coined the term `quantum quench', which became standard as well as being relevant for experiments on ultracold atoms.

Updated August 2023