Critical exponents of Manhattan Hamiltonian walks in two dimensions, from Potts andO(n) models

@article{Duplantier1987CriticalEO,
  title={Critical exponents of Manhattan Hamiltonian walks in two dimensions, from Potts andO(n) models},
  author={Bertrand Duplantier},
  journal={Journal of Statistical Physics},
  year={1987},
  volume={49},
  pages={411-431}
}
We consider a set of Hamiltonian circuits filling a Manhattan lattice, i.e., a square lattice with alternating traffic regulation. We show that the generating function (with fugacityz) of this set is identical to the critical partition function of aq-state Potts model on an unoriented square lattice withq1/2 =z. The set of critical exponents governing correlations of Hamiltonian circuits is derived using a Coulomb gas technique. These exponents are also found to be those of an O(n) vector model… CONTINUE READING