摘要: We consider quantum (unitary) continuous time evolution of spins on a lattice together with the itself. In physics such was discussed in connection gravity. It is also related to what called circuits, one incarnations computer. simpler models for which can obtain exact mathematical results. prove existence dynamics both Schroedinger and Heisenberg pictures, construct KMS states appropriate C*-algebras. show (for high temperatures) that each system where undergoes evolution, there natural scaling leading spin fixed lattice, defined by renormalized Hamiltonian.