A relation between the average length of loops and their free energy is obtained for a variety of O( n )-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number) averaged loop length stays finite for all non-zero fugacities n , and in particular it does not diverge upon entering the critical regime ( n 2 + ). Fully packed loop (FPL) models with n = 2 seem to obey the simple relation = 3 L min , where L min is the smallest loop length allowed by the underlying lattice. We demonstrate this analytically for the FPL model on the honeycomb lattice and for the 4-state Potts model on the square lattice, and based on numerical estimates obtained from a transfer matrix method we conjecture that this is also true for the two-flavour FPL model on the square lattice. We present, in addition, numerical results for the average loop length on the three critical branches (compact, dense and dilute) of the O( n ) model on the honeycomb lattice, and discuss the limit n 0. Contact is made with the predictions for the distribution of loop lengths obtained by conformal invariance methods.A relation between the average length of loops and their free energy is obtained for a variety of O( n )-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number) averaged loop length stays finite for all non-zero fugacities n , and in particular it does not diverge upon entering the critical regime ( n 2 + ). Fully packed loop (FPL) models with n = 2 seem to obey the simple relation = 3 L min , where L min is the smallest loop length allowed by the underlying lattice. We demonstrate this analytically for the FPL model on the honeycomb lattice and for the 4-state Potts model on the square lattice, and based on numerical estimates obtained from a transfer matrix method we conjecture that this is also true for the two-flavour FPL model on the square lattice. We present, in addition, numerical results for the average loop length on the three critical branches (compact, dense and dilute) of the O( n ) model on the honeycomb lattice, and discuss the limit n 0. Contact is made with the predictions for the distribution of loop lengths obtained by conformal invariance methods.

arXiv:cond-mat/9903242Journal of Physics A Mathematical and GeneralJan 1, 19995 citations

Deconfined quantum criticality in the 2D J-Q model

Bowen Zhao, Anders W. Sandvik

Bulletin of the American Physical SocietyMar 3, 20200 citations

Deconfined Criticality in a $J-Q$ model on Honeycomb latticeDeconfined Criticality in a $J-Q$ model on Honeycomb lattice

Sumiran Pujari, Fabien Alet, Kedar Damle

Bulletin of the American Physical SocietyMar 19, 20130 citations

High temperature series for the susceptibility of the Ising model. I. Two dimensional lattices

M F Sykes, David S. Gaunt, P D Roberts +1 more

Extended series expansions for the high temperature zero-field susceptibility of the Ising model are given in powers of the usual high temperature counting variable v=tanh K; for the triangular lattice to v 16 , for the square lattice to v 21 and for the honeycomb lattice to v 32 , inclusive. The asymptotic behaviour of the ferromagnetic and antiferromagnetic susceptibility is studied. It is concluded that the ferromagnetic singularity is not exactly factorizible. The antiferromagnetic susceptibility of the square and honeycomb lattices has a singularity of the same type as the energy at the antiferromagnetic critical temperature.Extended series expansions for the high temperature zero-field susceptibility of the Ising model are given in powers of the usual high temperature counting variable v=tanh K; for the triangular lattice to v 16 , for the square lattice to v 21 and for the honeycomb lattice to v 32 , inclusive. The asymptotic behaviour of the ferromagnetic and antiferromagnetic susceptibility is studied. It is concluded that the ferromagnetic singularity is not exactly factorizible. The antiferromagnetic susceptibility of the square and honeycomb lattices has a singularity of the same type as the energy at the antiferromagnetic critical temperature.

Journal of physics. A, Proceedings of the Physical Society. GeneralMay 1, 197290 citations

Thermal phase transitions to valence-bond-solid phase in the two-dimensional generalized SU(N) Heisenberg models

Takafumi J. Suzuki, Kenji Harada, Haruhiko Matsuo +2 more

We study thermal transitions of the generalized SU(N) Heisenberg models with four-body interactions on a square lattice and with six-body interactions on a honeycomb lattice. In both models for the N=3 and 4 cases, a singlet-dimer state is stabilized at a very low temperature, where a rotational symmetry of lattice is broken spontaneously. We discuss the universality class of thermal transition to the singlet dimer phases, performing quantum Monte Carlo calculations. From the finite-size scaling analysis, we find that the criticality for the square lattice case is well explained by the 2D weak Ising universality, while the 2D three-state Potts universality is observed in the honeycomb lattice case.We study thermal transitions of the generalized SU(N) Heisenberg models with four-body interactions on a square lattice and with six-body interactions on a honeycomb lattice. In both models for the N=3 and 4 cases, a singlet-dimer state is stabilized at a very low temperature, where a rotational symmetry of lattice is broken spontaneously. We discuss the universality class of thermal transition to the singlet dimer phases, performing quantum Monte Carlo calculations. From the finite-size scaling analysis, we find that the criticality for the square lattice case is well explained by the 2D weak Ising universality, while the 2D three-state Potts universality is observed in the honeycomb lattice case.

Journal of Physics Conference SeriesMar 18, 20150 citations

An investigation of the quantum J 1 - J 2 - J 3 model on the honeycomb lattice

J.-B. Fouet, Philippe Sindzingre, C. Lhuillier

arXiv:cond-mat/0101421The European Physical Journal BMar 1, 2001256 citations

Deconfined Criticality in a

J-Q

model on Honeycomb lattice