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We consider a two-dimensional electron or hole system at zero temperature andlow carrier densities, where the long-range Coulomb interactions dominate overthe kinetic energy. In this limit the clean system will form a Wigner crystal.Non-trivial quantum mechanical corrections to the classical ground state leadto multiparticle exchange processes that can be expressed as an effective spinHamiltonian involving competing interactions. Disorder will destroy the Wignercrystal on large length scales, and the resulting state is called a Wignerglass. The notion of multiparticle exchange processes is still applicable inthe Wigner glass, but the exchange frequencies now follow a randomdistribution. We compute the exchange frequencies for a large number ofrelevant exchange processes in the Wigner crystal, and the frequencydistributions for some important processes in the Wigner glass. The resultingeffective low energy spin Hamiltonian should be the starting point of ananalysis of the possible ground state phases and quantum phase transitionsbetween them. We find that disorder plays a crucial role and speculate on apossible zero temperature phase diagram.Comment: 17 pages and 12 figure

physical review. b, condensed matter

Multiparticle ring exchange in the Wigner glass and its possible relevance to strongly interacting two-dimensional electron systems in the presence of disorder