Checkerboard Lattice Research Articles

Ising model on a checkerboard lattice in a magnetic field H=1/2(iπkT)

The Lee-Yang formulae for the free energy and the magnetisation of the Ising model on a square lattice in an imaginary magnetic field H=1/2(iπkT) are generalised to a checkerboard lattice.

A disorder solution for a generalised mixed-spin model

A generalised mixed-spin model on a checkerboard square lattice is solved exactly along a trajectory in the parameter space by the use of an exact decimation method. A closed-form expression of the free energy per site is obtained and a criterion determining the validity of the solution is established.

The failure of a conjectured S4symmetry in the three-state checkerboard Potts model

Low-temperature expansions are obtained for the three-state Potts model on the checkerboard lattice. The four Boltzmann weights were set to various integer multiples of a low-temperature variable x. The series were evaluated to order x19 but it was found that the conjectured S4 symmetry failed at order x14 for the zero-field partition function, the spontaneous magnetisation and the zero-field susceptibility.

Critical correlations in a Z-invariant inhomogeneous ising model

We study the critical spin-spin correlation function in the Z-invariant inhomogeneous Ising model, which includes the rectangular, triangular, honeycomb, and checkerboard lattices as special cases. Using quadratic difference equations we derive various explicit representations for the correlation function, confirming and simplifying also a miraculous result of Baxter.

Two-dimensional Ising model with crossing and four-spin interactions and a magnetic fieldi(?/2)kT

The Ising model on a checkerboard lattice with crossing and four-spin interactions is solved exactly when there is pure imaginary magnetic fieldH=i(π/2)kT. The model exhibits a critical point with continuously varying exponents.

Exact results for a checkerboard Ising model with crossing and four-spin interactions

A seven-parameter Ising model with crossing and four-spin interactions on a checkerboard lattice is mapped by a duality transformation onto a general eight-vertex model, which has only five independent parameters. In a six-dimensional subspace of the Ising model (for which the corresponding eight-vertex model satisfies the free fermion condition) an exact solution is found.

Inversion relations and disorder solutions on Potts models

The inversion symmetry and the automorphy group generated by the latter, when combined with the spatial symmetries, are studied for the anisotropic Potts models on the triangular and checkerboard lattices. The exact expression of the partition function, which is known on some particular disorder subvarieties of the triangular model, is checked and a generalisation is proposed for the checkerboard lattice. The automorphy group is then used to extend the disorder solutions to the infinity of transformed subvarieties.

Q-state Potts model on the checkerboard lattice

A large q expansion of the partition function of the checkerboard q-state Potts model is given up to sixth order in q-12/. This expansion is used to discuss the following two points. First, on the critical manifold, the large q expansion agrees up to this order, with the 'minimal' solution suggested by the group structure associated with this model. Secondly, the latent heat and some correlation functions are discussed from the point of view of their functional dependence in the parameters.

Phase diagram of a simple model of Eu p Sr1?p S

A random site Ising model on the checkerboard square lattice with first neighbor interactionsJαβ in all first neighbor bonds and second neighbor interactionsJ ′ αβ in red squares is considered as a simple model of the dilute spin glass of Eu p Sr1−pS. The phase boundary between the paramagnetic and ferromagnetic phases, and that between the paramagnetic and spin glass phases are calculated. The obtained phase diagram is qualitatively similar to the experimental result by Maletta and Convert.