Density profiles, Casimir amplitudes, and critical exponents in the two-dimensional Potts model: A density-matrix renormalization study

We use the density matrix renormalization group (DMRG) to perform a detailed study of the critical properties of the two-dimensional $Q$ state Potts model, including the magnetization and energy-density profiles, bulk and surface critical exponents, and the Casimir amplitudes. We apply symmetry breaking boundary conditions to a $L\times \infty$ strip and diagonalize the corresponding transfer matrix for a series of moderately large systems $(L<~64)$ by the DMRG method. The numerically very accurate finite lattice results are then extrapolated by efficient sequence extrapolation techniques. The density profiles and the Casimir amplitudes at the critical point are found to follow precisely the conformal predictions for $Q=2\mathrm{}$ and $3$. Similarly, the bulk and surface critical exponents of the models are in very good agreement with the conformal and exact values: their accuracy has reached or even exceeded the accuracy of other available numerical methods. For the $Q=4\mathrm{}$ model both the profiles and the critical exponents show strong logarithmic corrections, which are also studied.