Tricritical behaviour in deterministic aperiodic Ising systems

Abstract

We use a mixed-spin model, with aperiodic ferromagnetic exchange interactions and crystalline fields, to investigate the effects of deterministic geometric fluctuations on first-order transitions and tricritical phenomena. The interactions and the crystal field parameters are distributed according to some two-letter substitution rules. From a Migdal-Kadanoff real-space renormalization-group calculation, which turns out to be exact on a suitable hierarchical lattice, we show that the effects of aperiodicity are qualitatively similar for tricritical and simple critical behaviour. In particular, the fixed point associated with tricritical behaviour becomes fully unstable beyond a certain threshold dimension (which depends on the aperiodicity), and is replaced by a two-cycle that controls a weakened and temperature-depressed tricritical singularity.

Formatting improved. 7 pages, 2 figures (included). Journal reference added

References in corpus (7)

• Critical Behavior of Random Bond Potts Models
• Real-Space Renormalization Group Study of the Two-dimensional Blume-Capel Model with a Random Crystal Field
• Quenched Randomness at First-Order Transitions
• Aperiodicity-Induced Second-Order Phase Transition in the 8-State Potts Model
• Universal Critical Behavior of Aperiodic Ferromagnetic Models
• Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions
• Strongly Asymmetric Tricriticality of Quenched Random-Field Systems

Cited by in corpus (2)

• Anisotropic Heisenberg model on hierarchical lattices with aperiodic interactions: a renormalization-group approach
• Critical behavior of spin and polymer models with aperiodic interactions