Spin chains and two-dimensional vertex models with an underlying superalgebra
structure appear naturally in certain statistical physics models,
e.g. intersecting loops, and disordered electron systems. In several examples
for such models the low energy effective theory describing their critical
behaviour has displayed rather unusual properties: the lack of unitarity in
these systems allows for continua of critical exponents leading to a fine
structure with strong subleading corrections to scaling in the finite size
spectrum. This is a signature of non-compact degrees of freedom emerging in
the continuum limit of these models.

In this project we plan to study the properties of these systems in the context of integrable superspin chains. In particular we want to identify the corresponding conformal field theories and characterize the continuous part of their spectrum. In addition, the effect of boundary conditions on the critical properties will be addressed. To deal with the strong finite-size effects present in these systems we shall develop new analytical methods for the analysis of the spectral problem.