Density-matrix renormalization-group technique with periodic boundary conditions for two-dimensional classical systems - art. no. 014401

The density-matrix renormalization-group (DMRG) method with periodic bounda ry conditions is introduced for two-dimensional (2D) classical spin models. It is shown that this method is more suitable for derivation of the proper ties of infinite 2D systems than the DMRG with open boundary conditions, de spite the fact that the latter describes much better strips of finite width . For calculation at criticality, phenomenological renormalization at finit e strips is used together with a criterion for optimum strip width for a gi ven order of approximation. For this width the critical temperature of the 2D Ising model is estimated with seven-digit accuracy for a not too large o rder of approximation. Similar precision is reached for critical exponents. These results exceed the accuracy of similar calculations for the DMRG wit h open boundary conditions by several orders of magnitude. The method is ap plied to the calculation of critical exponents of the q = 3,4 Ports model, as well.