Consider bond percolation on the square lattice and site percolation on the triangular lattice. Let κ(p) be the free energy at the zero field. If we assume the existence of the critical exponents for the three arm and four arm paths and these critical exponents are −2/3 and −5/4, respectively, then we can show the following power law for the free energy function κ(p): κ(p) = +(1/2− p) for p < 1...

The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular lattices is studied using the coupled cluster method (CCM) technique of quantum many-body theory. The phase relations between different expansion coefficients of the ground-state wave function in an Ising basis for the square lattice HAF is exactly known via the Marshall-Peierls sign rule, although no equivalent sign ru...

This paper introduces triangular wavelets, which are two-dimensional nonseparable biorthogonal wavelets defined on the regular triangular lattice. The construction that we propose is aimed at preserving isotropy, and a simple nonseparable extension of one-dimensional interpolating wavelets followed by a straightforward generalization. Resulting three oriented high-pass filters are symmetrically...

The coupled cluster method ~CCM! is applied to a spin-half model at zero temperature which interpolates between a triangular lattice antiferromagnet ~TAF! and a kagomé lattice antiferromagnet ~KAF!. The strength of the bonds which connect kagomé lattice sites is J, and the strength of the bonds which link the non-kagomé lattice sites to the kagomé lattice sites on an underlying triangular latti...

Magnetic property of antiferromagnets with two-dimensional distorted triangular lattice structures, β′-Me4P[Pd(dmit)2]2 and β′-Et2Me2P[Pd(dmit)2]2, was investigated by the muon spin relaxation method. Enhancement of the muon spin depolarization associated with the critical slow-down effect suggests that the spin dynamics due to the twoand three-dimensional magnetic correlations reflects the dev...

We apply a simple analytical criterion for locating critical temperatures to Potts models on square and triangular lattices. In the self-dual case, i. e. on the square lattice we reproduce known exact values of the critical temperature and derive the internal energy of the model at the critical point. For the Potts model on the triangular lattice we obtain very good numerical estimate of the cr...

A new model of population dynamics on lattices is proposed. The model consists of players on lattice points, each of which plays the RSP game with neighboring players. Each player chooses the next hand from the hand of the neighboring player with the maximum point. The model exhibits a steady pattern with pairs of vortices and sinks on the triangular lattice. It is shown that the stationary vor...

We compute in small temperature expansion the two-loop renormalization constants and the three-loop coefficient of the β-function, that is the first non-universal term, for the σ-model with O(N) invariance on the triangular lattice at N = −1. The partition function of the corresponding Grassmann theory is, for negative temperature, the generating function of unrooted forests on such a lattice, ...