Exact ground states of the extended Hubbard model on the Kagomé lattice

We discuss the exact plaquette-ordered ground states of the generalized Hubbard model on the Kagomé lattice for several fillings, by constructing the Hamiltonian as a sum of products of projection operators for up and down spin sectors. The obtained exact ground states are interpreted as Néel ordered states on the bond-located electrons. We determine several parameter regions of the exact ground states, and calculate the entanglement entropy. We examine the above results by numerical calculations based on exact diagonalization and density-matrix renormalization group methods.     

Influence of transverse field on the spin-3/2 Blume–Capel model on rectangular lattice

Transverse field effect on thermodynamic properties of the spin-3/2 Blume–Capel model on rectangular lattice in which the interactions in perpendicular directions differ in signs is studied within the mean field approximation. Phase diagrams in the (transverse field, temperature) plane are constructed for various values of single-ion anisotropy.     

Phase transitions and thermodynamic properties of antiferromagnetic Ising model with next-nearest-neighbor interactions on the Kagomé lattice

We study phase transitions and thermodynamic properties in the two-dimensional antiferromagnetic Ising model with next-nearest-neighbor interaction on a Kagomé lattice by Monte Carlo simulations. A histogram data analysis shows that a second-order transition occurs in the model. From the analysis of obtained data, we can assume that next-nearest-neighbor ferromagnetic interactions in two-dimensional antiferromagnetic Ising model on a Kagomé lattice excite the occurrence of a second-order transition and unusual behavior of thermodynamic properties on the temperature dependence.     

Low-energy singlets in the Heisenberg antiferromagnet on the kagomé lattice

The spin-1/2 Heisenberg antiferromagnet on the kagomé lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic T2 specific heat observed experimentally.     

The spin-1/2 J1–J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins

We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J₁-J₂ Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J₂/J₁. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J₂ < $J_2^{c_1}$ and J₂ > $J_2^{c_2}$ separated by a gapful quantum paramagnetic phase. We estimate $J_2^{c_1}$ ≈0.35J₁ and $J_2^{c_2}$ ≈0.66J₁.     

Magnetic correlations in the Hubbard model on triangular and Kagomé lattices

In order to study the magnetic properties of frustrated metallic systems, we present, for the first time, quantum Monte Carlo data on the magnetic susceptibility of the Hubbard model on triangular and kagomé lattices. We show that the underlying lattice structure determines the nature and the doping dependence of the magnetic fluctuations. In particular, in the doped kagomé case we find strong short-range magnetic correlations, which makes the metallic kagomé systems a promising field for studies of superconductivity.     

Néel order in the ground state of spin-1/2 Heisenberg antiferromagnetic multilayer systems

We show existence of Néel order for the ground state of a system withM two-dimensional layers with spin 1/2 and Heisenberg antiferromagnetic coupling, providedM8. The method uses the infrared bounds for the ground state combined with ideas introduced by Kennedy, Lieb, and Shastry.     

Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets

The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the spin-1/2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to ber times its value in the other two lattice directions. We prove the existence of Néel order for 0.16r1. For the 2D spin-1/2 model we give a series of inequalities which involve the two-point function only at short distances and each of which would by itself imply Néel order.     

Spin-liquid state for two-dimensional Heisenberg antiferromagnets on a kagomé lattice

The magnetic properties of the spin liquid state of the antiferromagnetic Heisenberg model on the kagomé lattice are investigated within the self-consistent mean-field theory. The results show that the spin liquid ground-state energy per site is , which is in very good agreement with the best numerical estimates. The spin structure factor and spin susceptibility are also discussed. Received 1 December 1998 and Received in final form 12 April 1999     

μSR study of the S=1/2 triangular lattice antiferromagnet AgNiO2

AgNiO₂, a model compound of an S=1/2 triangular lattice, was studied by muon spin relaxation in addition to ac, dc susceptibility, electrical resistivity and neutron diffraction. The relaxation rate shows a sharp peak at around T_N=28 K followed by a sudden decrease of initial asymmetry indicating a magnetic ordering. Three internal fields ranging from 0.2 to 0.3 T were obtained from the muon precession period. However, a neutron diffraction experiment failed to detect any magnetic order at low temperatures. From these results, it was concluded that magnetic coherence is confined to small domain compared with the coherence length of neutron diffraction due to spin frustration. This revised version was published online in August 2006 with corrections to the Cover Date.     

Computer simulation study of the two-dimensional nematic lattice model based on the modified Gruhn–Hess pair potential model

A modified Gruhn–Hess pair potential model, where the potential parameters related to the elastic constants are different from the original model, was investigated with the aid of Monte Carlo (MC) simulation and Mean Field (MF) theory based upon a two-dimensional nematic lattice model. The model produces a ground state in perfect nematic order, where particles are aligned in the lattice plane. Both the MF predictions and the simulation results for the second-rank ordering tensor show that the system is biaxial in the low-temperature region, with a positive primary order parameter and the main director aligned along the lattice axis. A transition to uniaxial order takes place at higher temperatures with a negative primary order parameter and the director is orthogonal to the lattice plane. This orientational order survives up to temperatures higher than the transition temperature of the three-dimensional lattice model, possibly at all finite temperatures. MF predictions agree qualitatively with simulation but, in quantitative terms, the transition temperature is overestimated by 52%.     

Position space renormalization group study of the spin-1 random semi-infinite Blume–Capel model

We study the spin-1 Blume–Capel model under a random crystal field in the tridimensional semi-infinite case. This has been done by using the real-space renormalization group approximation and specifically the Migdal–Kadanoff technique. Interesting results are obtained, which tell us that the randomness destroys the first order phase transitions and only those of the second order occur. We give the list of nine fixed points and their topology describing the surface critical behavior. Five new types of phase diagram are found with a rich variety of phase transitions, in accordance with the values of the bulk and surface probabilities and the ratios linking bulk and surface interactions.