chargelattice

Chargelattice is a theoretical construct in which electric charges occupy the sites of a fixed lattice and interact through Coulomb-like forces mediated along the lattice. It serves as a discrete model for ionic solids, electrolytes, and certain electronic systems where charge fluctuations are constrained by a lattice geometry.

In a typical formulation, a d-dimensional lattice with N sites hosts charges q_i at each site i. The charges may be restricted to integers or to a finite set of values, and the Hamiltonian includes long-range Coulomb interactions typically written via a lattice Green's function, often combined with short-range terms. Neutrality constraints (sum_i q_i = 0) are common. In lattice gauge-theory language, Gauss's law imposes a divergence constraint on the electric field, relating charges to lattice flux. Computational approaches include Monte Carlo methods and, for continuum limits, Ewald summation adapted to the lattice.

Variants include the lattice Coulomb gas, where only charges fluctuate and neutral configurations are sampled; and lattice dipole or spin models with emergent charge degrees of freedom. The charges may be dynamical (mobile carriers) or frozen to represent ionic sublattices. In two dimensions, the model connects to Kosterlitz-Thouless physics and to dual sine-Gordon descriptions in certain limits.

Applications and relevance include modeling ionic crystals, electrolytes, Wigner crystals in low-density electron systems, and some frustrated magnetic materials where magnetic charges obey similar lattice constraints. The chargelattice also serves as a testbed for algorithms dealing with long-range interactions on lattices.

Relation to continuum theories: as lattice spacing decreases, the discrete model approaches a continuum Coulomb gas; lattice artifacts can affect phase behavior and critical phenomena. See also Coulomb gas, lattice gauge theory, Wigner crystal, Gauss's law, Ewald summation.