Critical exponents of Manhattan Hamiltonian walks in two dimensions,from Potts andO(n) models |
| |
Authors: | Bertrand Duplantier |
| |
Institution: | (1) Service de Physique Théorique, CEN-Saclay, 91191 Gif-sur-Yvette, France |
| |
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. |
| |
Keywords: | Manhattan Hamiltonian walk critical exponents Potts O(n) SOS Coulomb gas conformal invariance surface exponents |
本文献已被 SpringerLink 等数据库收录! |
|