# Extra condition is necessary to have a unique cluster wave vectors set in the periodic cluster approximations - Condensed Matter > Disordered Systems and Neural Networks

Extra condition is necessary to have a unique cluster wave vectors set in the periodic cluster approximations - Condensed Matter > Disordered Systems and Neural Networks - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We added an extra condition, original lattice symmetry of chosen clusteraround cluster central site, to the cluster approximation methods with periodicboundary condition such as dynamical cluster approximation DCA, effectivemedium approximation EMSCA and nonlocal coherent potential approximationNLCPA. For each cluster size, this condition leads to a unique cluster wavevectors set in the first Brillouin zone FBZ where they preserve full symmetryof first Brillouin zone around ${\bf K=0}$. In this case whole cluster wavevectors are restricted to the FBZ and when number of sites in the cluster isequal to the whole lattice sites, these approximations recover original latticesymmetry in real and k-spaces.