Phase diagram of the triangular Ising model: Renormalization-group calculation with application to adsorbed monolayers

We study a triangular Ising model subject to nearest-neighbor pair interactions $K$, an external magnetic field $H$, and triangular three-spin interactions $P$. $K>\mathrm{}0\mathrm{} \mathrm{}(<0\mathrm{})\mathrm{}$ corresponds to ferromagnetic (antiferromagnetic) coupling. The phase diagram and thermodynamics are invariant under $\mathrm{}(K,H,P)\mathrm{}\leftrightarrow \mathrm{}(K,-H,-P)\mathrm{}$. A simple position-space renormalization group is formulated, based on three interpenetrating three-spin cells, which preserves the three-sublattice symmetry of the antiferromagnetic phase. The complete ($K,H,P$) phase diagram consists of five interconnecting transition surfaces (two second-order and three first-order), which bound the four single-phase regions (↑↑↑, ↑↑↓, ↑↓↓, and ↓↓↓). The edges of these surfaces form loci of second-order, critical-endpoint, and Baxter-Wu transitions. When $P=0\mathrm{}$, this system is known to provide a useful model of the order-disorder transition in monolayer films adsorbed on a hexagonal substrate. Calculation of the magnetization $M(K,H)\mathrm{}$ and heat capacity $c_M\mathrm{}(K,H)\mathrm{}$ of the Ising model allows quantitative comparison with experimental data for helium on graphite. The observed dependence $T_c\mathrm{}\left(n\right)\mathrm{}$ of the transition temperature on coverage is well fit with a single effective antiferromagnetic pair interaction. The corresponding calculated heat capacities (no additional adjustable parameters) are in remarkable agreement with experimental data near and below $T_c$.