# 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

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