Theory of critical phenomena

  • PI: Delfino

Statistical systems can exhibit critical points characterized by collective phenomena and emergent universal properties. The latter do not depend on the microscopic details of the system, but are dictated by its symmetries and dimensionality. This circumstance makes field theory the natural framework for studying critical phenomena and universality.

Field theory also explains why the scale invariance induced at criticality by the diverging correlation length is actually promoted to invariance under a larger group of transformations, the conformal group. Conformal invariance is a powerful tool that gives access to many exact results. A different source of exact results is provided by low-energy properties of field theory in problems (separation of phases, formation of vortices, …) involving a hierarchy of length scales (microscopic scale, correlation length, system size).

We develop these and other ideas and apply them to several facets of the theory of critical phenomena. Those on which we are currently focusing include:

  • Percolation and other instances of geometrical phase transitions
  • Systems with quenched disorder and random critical points
  • Phase separation, interfaces and wetting
  • Quantum quenches near criticality
  • Topological excitations

A list of recent results can be found here.

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