Density Profiles, Casimir Amplitudes and Critical Exponents in the Two Dimensional Potts Model: A Density Matrix Renormalization Study

Abstract

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 ($L\le 64$) by the DMRG method. The numerically very accurate finite lattice results are then extrapolated by efficient sequence extrapolation techniques. The critical density profiles and the Casimir amplitudes are found to follow precisely the conformal predictions for Q=2 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 model both the profiles and the critical exponents show strong logarithmic corrections, which are also studied.

12 pages, RevTeX, 14 PostScript figures included

References in corpus (6)

• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Casimir forces in binary liquid mixtures
• Effect of Gravity and Confinement on Phase Equilibria: A Density Matrix Renormalization Approach
• The phase diagram of magnetic ladders constructed from a composite-spin model
• Density matrix renormalization group for the Berezinskii-Kosterlitz-Thouless transition of the 19-vertex model
• Corner Exponents in the Two-Dimensional Potts Model

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• Logarithmic delocalization of end spins in the S=3/2 antiferromagnetic Heisenberg chain
• Interfacial adsorption in two-dimensional Potts models
• Critical Behavior of the Random Potts Chain
• Analysis of a continuous field theory in two dimensions with use of the Density Matrix Renormalization Group
• The density of critical percolation clusters touching the boundaries of strips and squares
• Entanglement entropy of the $Q\ge 4$ quantum Potts chain
• Density of critical clusters in strips of strongly disordered systems
• Coexistence of excited states in confined Ising systems
• Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem
• Conformal off-diagonal boundary density profiles on a semi-infinite strip