Closed-form solutions and free energy of hard-spin mean-field theory of a fully frustrated system

Closed-form solutions of the hard-spin mean-field theory equations for the antiferromagnetic Ising model on a triangular lattice, with or without an external field H, are obtained, showing the lack of order for H=0 and very good agreement with Monte Carlo data for the onset of order for nonzero H. A free energy calculation is developed, within the context of hard-spin mean-field theory, distinguishing between metastable solutions and true thermodynamic equilibrium. © 1994 The American Physical Society

Tricritical behaviour in deterministic aperiodic Ising systems

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.Comment: Formatting improved. 7 pages, 2 figures (included). Journal reference adde