Antiferromagnetic XY Model Research Articles

Mean field theory of superconductivity in frustrated 2D-XY magnets

We consider the two-dimensional antiferromagnetic classical XY model on a square lattice with frustrated plaquettes introduced by dilute doping of ferromagnetic bonds. These ferromagnetic bonds carry positive electronic charges of the holes. A pairing potential is derived and the energy spectrum of a hole pair is discussed for the possibility of bound states. In the long distance approximation, the dipolar interaction between canted local states is derived and discussed in the mean field in both reciprocal space and real space. BCS type calculation of the pairing potential is formulated for the lowest angular momentum gap function. The odd parity gap yields higher transition temperature then the corresponding even parity one. Application to La 2CuO 4 yields critical temperature in the order of 40 K. Implications of this effective attraction mediated by the frustrated plaquettes in the XY model are suggested for other types of two-dimensional magnets. Possible extensions of the model to incorporate Ising anisotropy and interplanar coupling are discussed.

MAGNETIC PAIRING IN TWO-DIMENSIONAL ANTIFERROMAGNETIC XY MODEL

A two-dimensional Ising Coulomb gas is introduced to describe the frustrated plaquettes of the two-dimensional antiferromagnetic XY model with Coulomb repulsion. The Ising spin variable corresponds to the two possible chiralities of the frustrated plaquettes, which repel each other with a screened Coulomb potential. Using the self-consistent screening analysis, the Ising Coulomb gas is shown to have a Kosterlitz-Thouless transition from a pairing phase at low temperature to a plasma phase at high temperature. The phase diagram is obtained numerically as a function of density and relative strength of the attraction between particles of opposite chiralities and the Coulomb repulsion. Possible applications to the magnetic pairing mechanism of high temperature superconductors is discussed in the context of Li doped La 2 CuO 4. It is also argued that the Aharony et al. model of magnetic pairing with the dipolar attraction can be derived as a special case of the Ising Coulomb gas model and is superceded by a stronger attractive interaction in magnetic pairing mechanism in the self-consistent analysis.

Statistical Mechanical Theory of Cooperative Phenomena. II. Super-Effective-Field Theory with Applications to Exotic Phase Transitions

A new scheme to study exotic phase transitions is formulated by introducing the concept of a super-effective field. A general mechanism of phase transitions is elucidated and a general criterion of order parameters is proposed on the basis of the newly formulated super-effective-field theory. An alternative formulation based on a decoupled density matrix is also given. It is easily shown using these formulations that a quantum chiral order appears in the antiferromagnetic XY model on the triangular lattice. A super-effective-field theory of spin glasses is also presented.

Zero-temperature ordering in the two-dimensional quantum XY model

We have calculated the probability distribution for the staggered magnetization at T=0 for the 2D antiferromagnetic quantum XY model on finite lattices. For the ground state, the distribution shows evidence of isotropic magnetization ordering on the xy-plane. Based on data on seven lattices up to 26 sites, the extrapolated value of the staggered magnetization is 0.448±0.003 in the thermodynamic limit.

Renormalization group approach to antiferromagnetic quantum XY model on a triangular lattice

Renormalization group approach to antiferromagnetic quantum XY model on a triangular lattice

Exact real space renormalisation group transformation for the dimerised XY chain

An analytical real space renormalisation group transformation is obtained for the one-dimensional spin-1/2 antiferromagnetic dimerised XY model. Using the method of Sarker (1984) the recursion relations for the parameters are derived from the mapping between blocks of sizes L and L/b, for arbitrary size L and scale factor b. The results for the gap and for the critical exponent are shown to converge rapidly toward their exact values. The dynamical exponent has 1/L corrections (b approximately 1) instead of the usual 1/ln L ones (b=L). The differential renormalisation group equations are obtained explicitly. The authors show that the non-analyticity of the scaling function (for the density of energy) stems from a dangerous irrelevant variable, the antiferromagnetic coupling.

Phase diagram of the antiferromagnetic XY model with a triangular lattice in an external magnetic field

The ordered states of a planar antiferromagnet with a triangular lattice are investigated in the presence of a magnetic field. The spin wave free energy is taken into account and proved to be important for determining the properties of the system. The phase diagram is constructed. It contains four different phases with rigorous long-range order. Three of them are characterised by different configurations of mean magnetic moments for the three substances. The existence of one or more non-trivial phase with an algebraic decay of the correlation functions is very probable.