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Solvable Lattice Models and Integrable Quantum Field Theories
The solvable lattice models referred to are certain classical two-dimensional
statistical-mechanical models that admit an exact solution; the quantum
field theories are two-dimensional models
which can be considered as `toy models' for the four-dimensional quantum
field theories that describe sub-atomic particles.
It turns out that an integrable quantum field theory can often be
considered as the continuum limit of a solvable lattice model. Underlying
both types of system are certain algebraic symmetries that are responsible
for the epithets `solvable' and `integrable'. A PhD student is sought to
work on using these algebraic symmetries in order to obtain exact solutions
of such models. The student should have an interest in mathematical or
theoretical physics.