Phase boundary of Ising antiferromagnets nearH=HcandT=0: Results from hard-core lattice gas calculations

Ising antiferromagnets in a near-critical magnetic field at low temperatures are equivalent to hard-core lattice gases. Using this connection and the existing series-expansion results for hard-core lattice gases, we determine the slope of the phase boundary at $T=0\mathrm{}$ for the square (sq), plane-triangular (pt), simple cubic (sc), and body-centered cubic (bcc) antiferromagnets. The slope is negative for the sq and pt lattices and nearly zero for the sc case. For the bcc lattice a positive slope is obtained, indicating that the phase boundary bulges above the zero-temperature critical field. We also test Müller-Hartmann and Zittarz's postulate for the critical curve of the sq Ising antiferromagnet. A renormalization-group treatment of the hard-square lattice gas yields a critical activity $z^{*}=3.7959\mathrm{}\pm 0.0001$, which is in agreement with series-expansion and finite-lattice estimates but at variance with the postulated $z^{*}=4\mathrm{}$. The same calculation gives $\nu =0.999\mathrm{}\pm 0.001$ for the correlation-length exponent, thus supporting the conjecture that the transition of the hard-square lattice gas belongs to the Ising universality class.