Percolation due to the simultaneous occupation of two neighboring bond sites, namely a bond dimer, is considered here by means of the renormalization cell technique providing an analytic way to obtain results such as percolation threshold, jamming coverage and critical exponents. This is...

Magnetic frustration in the framework of the Edwards–Anderson model is studied for the ground level (T=0) of the Kagomé lattice (KL). A sample consists of a realization of a random distribution of ferromagnetic (F) and antiferromagnetic (AF) interactions of the same strength along lines...

Method of the sublattice previously introduced for homogeneous lattices is adapted here to characterize ground state properties of two inhomogeneous lattices: Kagomé lattice with coordination 4 and Five-points-star lattice with coordination 5. A representative cell must be chosen in each case...

Bond percolation is studied for the three homogeneous two-dimensional lattices: square lattice (SL), triangular lattice (TL) and honeycomb lattice (HL). An expanding cell technique is used to obtain percolation thresholds and other relevant information for different cell sizes. We extend the...

We report results on ground state properties for a ±J Ising model defined on the Archimedean (4,82) lattice. The sublattice method is adapted to this system. By means of combinatorics and probability analysis, weight functions are obtained allowing to calculate properties such as frustrated...

A theoretical approach, based on exact calculations of configurations on finite rectangular cells, is applied to study the percolation of homonuclear dimers on square lattices. An efficient algorithm allows us to calculate the detailed structure of the configuration space for M=Lx×Ly cells,...

We report the main results on ground state properties for a ±J Ising model defined on a Dice lattice. The sublattice method is adapted to this non-Archimedean system. By means of combinatorics and probability analysis, weight functions are obtained allowing to calculate properties such as...

Physical magnitudes of ±J Ising systems are determined by their topological properties which depend on the number of frustrated plaquettes and on the distribution of curved plaquettes through the lattice. In the present paper, we consider two-dimensional lattices (3 homogeneous and 3 mixed...

This paper tackles the problem of finding analytical expressions describing the ground state properties of Dürer lattices over which a generalized Edwards–Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for these lattices....

This paper addresses the problem of finding analytical expressions describing the ground state properties of mixed Archimedean lattices over which a generalized Edwards–Anderson model (±J Ising model) is defined. A local frustration analysis is performed based on representative cells for...