Dedecoration as a renormalization group transformation for linear Ising chain

Kenjirô Kambe

Uli Deker, Fritz Haake

David R. Nelson, Michael Ellis Fisher

Renormalization groups are constructed in exact closed form (as finite‐dimensional recursion relations) for a range of one‐dimensional Ising models including staggered and parallel magnetic fields, alternating and second neighbor pair coupling, four‐spin interactions, etc. Linearization about appropriate fixed points displays relevant, irrelevant, and marginal operators and yields the exact scaling behavior about the T=0 critical point (where η=1, δ=∞, and γ=ν). Both a fixed spin “dedecoration” group (based on the bond decoration process) and a spin‐rescaling group give identical critical behavior; but they lead to distinct realizations of the nonlinear scaling fields appearing in Wegner's analysis of corrections to scaling (which has been extended to discrete groups). The spin dedecoration and star‐triangle transformations are used to analyze a planar, multiconnected, “truncated tetrahedron” model.

Wim van Saarloos, J. M. J. van Leeuwen, Attilio L. Stella

J. C. Cressoni, Roberto J. V. dos Santos

The linear Z(3) spin system in the presence of a magnetic field is studied by a dedecoration renormalisation group (RG) transformation. In order to perform the transformation, non-usual terms must be added to the Hamiltonian. The linear region around a particular T=0 fixed point, where these terms go to zero, is investigated and the 'critical behaviour' of the free energy, correlation function and susceptibility is obtained. The system is solved exactly and the results are compared with those obtained by the RG approach. Magnetisation and susceptibility curves against temperature are also shown.

I. P. Fittipaldi, Douglas F. de Albuquerque