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

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Abstract

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 withq 1/2 =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 in the low-temperature phase withn =q 1/2 =z. The critical exponents in the limitz = 0 are then those of spanning trees (q= 0) and of dense polymers (n=0,T < Tc), corresponding to a conformal theory with central chargeC = −2. This shows that the Manhattan orientation and the Hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of Hamiltonian walks.

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  1. Service de Physique Théorique, CEN-Saclay, 91191, Gif-sur-Yvette, France

    Bertrand Duplantier

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  1. Bertrand Duplantier
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Duplantier, B. Critical exponents of Manhattan Hamiltonian walks in two dimensions, from Potts andO(n) models. J Stat Phys 49, 411–431 (1987). https://doi.org/10.1007/BF01009343

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