Complete Density Calculations of q-State Potts and Clock Models: Reentrance of Interface Densities under Symmetry Breaking

Abstract

All local bond-state densities are calculated for q-state Potts and clock models in three spatial dimensions, d=3. The calculations are done by an exact renormalization group on a hierarchical lattice, including the density recursion relations, and simultaneously are the Migdal-Kadanoff approximation for the cubic lattice. Reentrant behavior is found in the interface densities under symmetry breaking, in the sense that upon lowering temperature the value of the density first increases, then decreases to its zero value at zero temperature. For this behavior, a physical mechanism is proposed. A contrast between the phase transition of the two models is found, and explained by alignment and entropy, as the number of states q goes to infinity. For the clock models, the renormalization-group flows of up to twenty energies are used.

Published version, 8 pages, 7 figures, 1 table

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Cited by in corpus (9)

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• Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line
• Thermodynamical behavior of the Blume-Capel model in the vicinity of its tricritical point
• Renormalization-Group Theory of the Heisenberg Model in d Dimensions
• Phase Transitions of the Variety of Random-Field Potts Models
• Spin-s Spin-Glass Phases in the d=3 Ising Model
• Across Dimensions: Two- and Three-Dimensional Phase Transitions from the Iterative Renormalization-Group Theory of Chains
• Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory
• Metastable Potts Droplets