###### M2 Second semester, courses

## Statistical field theory of complex matter

**Closed in 2020-21**

Statistical field theory (SFT) applies ordinarily to systems close to a critical phase transition, where large-scale fluctuations are observed. However, complex materials often exhibit strong thermal fluctuations simply because of their softness. As the number of symmetries in nature is limited, these systems are described by the same SFT tools as critical systems, and thus often exhibit critical exponents and scaling laws. For instance, the partition function of a self-avoiding walk or polymer is a path integral that can be mapped onto a quantum particle Schrödinger probability amplitude, then onto a Gaussian correlation function, then back to an

*O(n)*model in the replica*n→0*limit. Thus polymers share the same exponents as magnets. In the*O(n)*models, the field are vectors, but what if they become tensorial? We may use again our SFT skills and end up describing the liquid crystal ordering that lies within your computer screen. This what physics is about: describing a large variety of phenomena with a limited number of concepts and tools.**Bibliography**

*Principles of Condensed Matter Physics*, P. Chaikin and T. C. Lubensky, Cambridge University Press.*The Physics of Liquid Crystals*, P.-G. de Gennes & J. Prost, Oxford Science Publications.*Scaling Concepts in Polymer Physics*, P.-G. de Gennes, Cornell University Press.

Jean-Baptiste Fournier

(Université Paris Diderot)

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