Non-scalar operators for the Potts model in arbitrary dimension

Understand

We investigate the operator content of the Q-state Potts model in arbitrary dimension, using the representation theory of the symmetric group.

• In particular we construct all possible tensors acting on N spins, corresponding to given symmetries under $S_Q$ and $S_N$, in terms of representations involving any Young diagram.
• These operators transform non-trivially under the group of spatial rotations, with a definite conformal spin.
• The two-point correlation functions are then computed, and their physical interpretation is given in terms of Fortuin-Kasteleyn clusters propagating between two neighbourhoods of each N spins.