Corner Transfer Matrix Algorithm for Classical Renormalization Group

1997/05/08 by Tomotoshi Nishino, Kouichi Okunishi · 5 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1143/jpsj.66.3040

published as J. Phys. Soc. Jpn. 66 (1997) 3040 · 20 pages, 10 ps figures, JPSJ style files are included

arxiv created 1997/05/08 · openalex publication_date 1997/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group transformation according to White's density matrix algorithm, so that variational free energies are minimized within a restricted degree of freedom m. As a consequence of the renormalization, spin variables on each corner of CTM are replaced by a m-state block spin variable. It is shown that the thermodynamic functions and critical exponents of the q = 2, 3 Potts models can be precisely evaluated by use of the renormalization group method.

Citations

• The renormalization group and the ε expansion
• On the product of semi-groups of operators
• Density-matrix algorithms for quantum renormalization groups
• Some generalized order-disorder transformations

Cited by

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• Phase transition of clock models on a hyperbolic lattice studied by corner transfer matrix renormalization group method
• QUANTUM CORNER — TRANSFER MATRIX DMRG
• New trends in density matrix renormalization
• Numerical renormalization approach to two-dimensional quantum antiferromagnets with valence-bond-solid type ground state