Density matrix and renormalization for classical lattice models.

The density matrix renormalization group is a variational approximation method that maximizes the partition function — or minimize the ground state energy — of quantum lattice systems. The variational relation is expressed as Z=Trρ≥Tr ( $$\tilde 1$$ ρ), where ρ is the density submatrix of the system, and $$\tilde 1$$ is a projection operator. In this report we apply the variational relation to two-dimensional (2D) classical lattice models, where the density submatrix ρ is obtained as a product of the corner transfer matrices. The obtained renormalization group method for 2D classical lattice model, the corner transfer matrix renormalization group method, is applied to the q=2∼5 Potts models. With the help of the finite size scaling, critical exponents (q=2, 3) and the latent heat (q=5) are precisely obtained. [ABSTRACT FROM AUTHOR]