Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line

Abstract

The random-field XY model is studied in spatial dimensions d=3 and 4, and in-between, as the limit q --> \infty of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower-critical dimension is determined between 3.81 < d_c <4. When the random-field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random-field is scaled with q^2, a universal phase diagram is found at intermediate temperatures in d=3.

4 pages, 15 phase diagrams

References in corpus (3)

• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• First-Order to Second-Order Phase Transition Changeover and Latent Heats of q-State Potts Models in d=2,3 from a Simple Migdal-Kadanoff Adaptation
• Renormalization-Group Theory of the Heisenberg Model in d Dimensions

Cited by in corpus (7)

• Complex dynamics approach to dynamical quantum phase transitions: the Potts model
• Thermodynamical behavior of the Blume-Capel model in the vicinity of its tricritical point
• Renormalization-Group Theory of the Heisenberg Model in d Dimensions
• Critical behaviours of anisotropic XY ferromagnet in the presence of random field
• Nematic Ordering in the Heisenberg Spin-Glass System in d=3 Dimensions
• Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory
• XY-Ashkin-Teller Phase Diagram in d=3