Ising magnets with frustration: Zero-temperature properties from series expansions

Abstract

We study a quenched random Ising magnet with mixed nearest-neighbor exchange couplings $\pm J$ on the square (sq), triangular (t), and simple-cubic (sc) lattices. We derive expansions for the $T=0\mathrm{}$ thermodynamic properties in the ferromagnetic phase in powers of the concentration $p$ of antiferromagnetic couplings. Analysis of these series in the variable $c$, which measures the concentration of frustrated plaquettes, indicates that ferromagnetism disappears at a second-order phase transition with $p_c\left(\mathrm{sq}\right)\approx 0.099$, $p_c\left(\mathrm{t}\right)=0.10-0.15\mathrm{}$, and $p_c\left(\mathrm{sc}\right)=0.12-0.13\mathrm{}$. The square-lattice series, which are the best behaved, suggest that (i) the magnetization vanishes with a critical exponent ${\beta }_M\left(\mathrm{sq}\right)\approx 0.066$, and (ii) the phase for $p>\mathrm{}{p}_c$ may exhibit Edwards-Anderson order.