Lattice actions improved by block-spin renormalisation group and maximally symmetric lattices

We adapt White's density matrix renormalisation group (DMRG) to the direct study of critical phenomena. We use the DMRG to generate transformations in the space of coupling constants. We postulate that a study of density matrix eigenvalues leads to a natural identification of renormalised blocks, operators and Hamiltonians. We apply the scheme to the phase transition in the anisotropic spin-1/2 Heisenberg chain. In the simplest case where the two most probable states in odd sized blocks are used to construct approximate renormalisation group transformations, we find qualitative improvement upon the standard real space renormalisation group method for the thermal exponent $ν$ .We adapt White's density matrix renormalisation group (DMRG) to the direct study of critical phenomena. We use the DMRG to generate transformations in the space of coupling constants. We postulate that a study of density matrix eigenvalues leads to a natural identification of renormalised blocks, operators and Hamiltonians. We apply the scheme to the phase transition in the anisotropic spin-1/2 Heisenberg chain. In the simplest case where the two most probable states in odd sized blocks are used to construct approximate renormalisation group transformations, we find qualitative improvement upon the standard real space renormalisation group method for the thermal exponent $ν$.

arXiv:cond-mat/9511045Nov 9, 19950 citations

Non-perturbative renormalization-group approach to lattice models

N. Dupuis, K. Sengupta

arXiv:0806.4257The European Physical Journal BNov 1, 200817 citations

Renormalisation group calculations on a mixed-spin system in two dimensions

S. L. Schofield, Roger Bowers

The real space renormalisation group of Niemeijer and van Leeuwen (1974) is applied to a mixed-spin Ising model on a simple quadratic lattice. The motivation is the investigation of critical phenomena in Ising models with less than the usual translational symmetry. The models in question are relevant to the study of ferrimagnetism. Two calculations, characterised by different block constructions, are performed and compared. Exponent values are found to be in good agreement with those suggested by the universality hypothesis. The utility of the renormalisation group for dealing with ferrimagnetism is demonstrated, but the high degree of labour involved in such an exercise is indicated.The real space renormalisation group of Niemeijer and van Leeuwen (1974) is applied to a mixed-spin Ising model on a simple quadratic lattice. The motivation is the investigation of critical phenomena in Ising models with less than the usual translational symmetry. The models in question are relevant to the study of ferrimagnetism. Two calculations, characterised by different block constructions, are performed and compared. Exponent values are found to be in good agreement with those suggested by the universality hypothesis. The utility of the renormalisation group for dealing with ferrimagnetism is demonstrated, but the high degree of labour involved in such an exercise is indicated.

Journal of Physics A Mathematical and GeneralDec 1, 198074 citations

A transformation of lattice spin operators

H. J. Hilhorst

Physics Letters AMay 1, 19741 citation

Optimised renormalisation group transformations of lattice spin models

Andrew F. Bennett

The optimisation of real space renormalisation group transformations is explored in the framework of series expansions. A block-spin transformation (in addition to decimation) is constructed which exactly maps the one-dimensional nearest-neighbour Ising model onto itself. The same construction can also be applied to the q-state Potts model. In higher dimensions, similar optimisation can be achieved only if the weight function has interactions of range comparable to those generated in the series expansion.The optimisation of real space renormalisation group transformations is explored in the framework of series expansions. A block-spin transformation (in addition to decimation) is constructed which exactly maps the one-dimensional nearest-neighbour Ising model onto itself. The same construction can also be applied to the q-state Potts model. In higher dimensions, similar optimisation can be achieved only if the weight function has interactions of range comparable to those generated in the series expansion.

Journal of Physics A Mathematical and GeneralOct 1, 19871 citation

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