Critical behaviour of the fully packed loop model on the square lattice

We investigate the critical behaviour of the fully packed O(n) loop model on the square lattice in which each vertex is visited once by a loop. A transfer-matrix analysis shows that this model can be interpreted as a superposition of a low-temperature O(n) model and an solid-on-solid (SOS) model, as for the fully packed model on the honeycomb lattice. However, not all of the critical exponents are the same for both lattices. In contrast, the fully packed model on the triangular lattice appears to behave as a pure low-temperature O(n) model.

[1]  M. N. Barber,et al.  Conformal invariance, the XXZ chain and the operator content of two-dimensional critical systems , 1988 .

[2]  K. Seaton,et al.  Surface critical behaviour of an O(n) loop model related to two Manhattan lattice walk problems , 1995 .

[3]  Elliott H. Lieb,et al.  Residual Entropy of Square Ice , 1967 .

[4]  I. Affleck.  Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly , 1986 .

[5]  Henley,et al.  Conformal charge and exact exponents in the n=2 fully packed loop model. , 1994, Physical Review Letters.

[6]  H. Blote,et al.  Critical behaviour and conformal anomaly of the O(n) model on the square lattice , 1989 .

[7]  W. J. C. Orr,et al.  Statistical treatment of polymer solutions at infinite dilution , 1947 .

[8]  Blöte,et al.  Fully packed loop model on the honeycomb lattice. , 1994, Physical review letters.

[9]  B. Duplantier.  Exact critical exponents for two-dimensional dense polymers , 1986 .

[10]  Anthony J. Guttmann,et al.  The size and number of rings on the square lattice , 1988 .

[11]  J. Cardy,et al.  Conformal invariance, the central charge, and universal finite-size amplitudes at criticality. , 1986, Physical review letters.

[12]  Suzuki,et al.  Exact results for Hamiltonian walks from the solution of the fully packed loop model on the honeycomb lattice. , 1994, Physical review letters.

[13]  J. Cardy,et al.  Conformal invariance and universality in finite-size scaling , 1984 .

[14]  Y. Oono,et al.  Walks, trials and polymers with loops , 1984 .

[15]  Huse,et al.  Classical antiferromagnets on the Kagomé lattice. , 1992, Physical review. B, Condensed matter.

[16]  E. Domany,et al.  Duality relations and equivalences for models with O(N) and cubic symmetry , 1981 .

[17]  D. Klein,et al.  Compact self-avoiding circuits on two-dimensional lattices , 1984 .