C Tsallis 1985 J. Phys. C: Solid State Phys. 18 6581 doi:10.1088/0022-3719/18/36/013
C Tsallis
Show affiliationsCertain types of real-space renormalisation groups (which essentially approximate Bravais lattices through hierarchical ones) do not preserve standard thermodynamic convexity properties. The author points out that this serious defect is not intrinsic to any real-space renormalisation. It can be avoided if form invariance (under uniform translation of the energy scale) of the equation connecting the Bravais lattice (which he intends to study) to the hierarchical one (which approximates it) is demanded. In addition to this he analyses expressions for the critical exponents nu and alpha corresponding to hierarchical lattices; these are consistent with recent analysis by Melrose (1983) of the fractal intrinsic dimensionality, which he considers to be correct in order for hyperscaling to hold for hierarchical lattices.
61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
Issue 36 (30 December 1985)
C Tsallis 1985 J. Phys. C: Solid State Phys. 18 6581
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