The global phase diagrams of the corner cubic anisotropic discrete-spin Heisenberg (CH) model and its site-diluted version (dCH) on a triangular lattice are investigated through the position-space renormalization-group method of the simple Migdal-Kadanoff type. The two models include many simpler models as their subspaces, and the interrelations among these models are elucidated. The five-dimensional (5D) phase diagram of the dCH model is generated from the 3D one of the CH model by introducing 2D site-dilution operation. The structure of the 5D phase diagram and the effect of site dilution on the CH model are conveniently visualized by introducing the concept of paths in the 3D subspace. The path describes the temperature variation provided that the ratios between the interaction parameters in the original CH model are fixed. The resulting phase diagrams of the dCH model exhibit the typical three-phase coexistence of solid, liquid, and gas, and their qualitative interpretations are summarized.The global phase diagrams of the corner cubic anisotropic discrete-spin Heisenberg (CH) model and its site-diluted version (dCH) on a triangular lattice are investigated through the position-space renormalization-group method of the simple Migdal-Kadanoff type. The two models include many simpler models as their subspaces, and the interrelations among these models are elucidated. The five-dimensional (5D) phase diagram of the dCH model is generated from the 3D one of the CH model by introducing 2D site-dilution operation. The structure of the 5D phase diagram and the effect of site dilution on the CH model are conveniently visualized by introducing the concept of paths in the 3D subspace. The path describes the temperature variation provided that the ratios between the interaction parameters in the original CH model are fixed. The resulting phase diagrams of the dCH model exhibit the typical three-phase coexistence of solid, liquid, and gas, and their qualitative interpretations are summarized.

Physical review. B, Condensed matterFeb 1, 19852 citations

Nonperturbative real-space renormalization group scheme for the spin- 12 XXXHeisenberg model

Andreas Degenhard

In this paper we apply an analytical real-space renormalization group formulation which is based on numerical concepts of the density-matrix renormalization group. Within a rigorous mathematical framework we construct nonperturbative renormalization group transformations for the spin- $\frac{1}{2}$ $\mathrm{XXX}$ Heisenberg model in the finite-temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behavior in the temperature-dependent coupling constant. The constructed renormalization group transformations are applied within the ferromagnetic and the antiferromagnetic regime of the Heisenberg chain. The ferromagnetic fixed point is computed and compared to results derived by other techniques.In this paper we apply an analytical real-space renormalization group formulation which is based on numerical concepts of the density-matrix renormalization group. Within a rigorous mathematical framework we construct nonperturbative renormalization group transformations for the spin-$\frac{1}{2}$ $\mathrm{XXX}$ Heisenberg model in the finite-temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behavior in the temperature-dependent coupling constant. The constructed renormalization group transformations are applied within the ferromagnetic and the antiferromagnetic regime of the Heisenberg chain. The ferromagnetic fixed point is computed and compared to results derived by other techniques.

arXiv:cond-mat/9910512Physical review. B, Condensed matterOct 3, 20014 citations

Renormalization group solution of the one-dimensional classical Heisenberg model

Th. Niemeijer, Th.W. Ruijgrok

Physica A Statistical Mechanics and its ApplicationsJan 1, 19756 citations

Renormalization-group studies of antiferromagnetic chains. I. Nearest-neighbor interactions

Jeffrey M. Rabin

The real-space renormalization-group method introduced by workers at the Stanford Linear Accelerator Center (SLAC) is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation, a duality transformation is introduced under which the isotropic Heisenberg model is self-dual. Such duality transformation can be defined for models other than those considered here, and may be useful in various block-spin calculations.The real-space renormalization-group method introduced by workers at the Stanford Linear Accelerator Center (SLAC) is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation, a duality transformation is introduced under which the isotropic Heisenberg model is self-dual. Such duality transformation can be defined for models other than those considered here, and may be useful in various block-spin calculations.

Physical review. B, Condensed matterMar 1, 198040 citations

Renormalization-Group Theory of the Heisenberg Model in D Dimensions

A. Nihat Berker, Egemen Tunca

Jan 1, 20220 citations

\frac{1}{2}

\mathrm{XXX}

Heisenberg model in the finite-temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behavior in the temperature-dependent coupling constant. The constructed renormalization group transformations are applied within the ferromagnetic and the antiferromagnetic regime of the Heisenberg chain. The ferromagnetic fixed point is computed and compared to results derived by other techniques.