TY - JOUR

T1 - Phase boundary of Ising antiferromagnets near H=Hc and T=0

T2 - Results from hard-core lattice gas calculations

AU - Ràcz, Zoltàn

PY - 1980/1/1

Y1 - 1980/1/1

N2 - 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 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 M̈ller-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±0.0001, which is in agreement with series-expansion and finite-lattice estimates but at variance with the postulated z*=4. The same calculation gives 1/2=0.999±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.

AB - 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 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 M̈ller-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±0.0001, which is in agreement with series-expansion and finite-lattice estimates but at variance with the postulated z*=4. The same calculation gives 1/2=0.999±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.

UR - http://www.scopus.com/inward/record.url?scp=0000732416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000732416&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.21.4012

DO - 10.1103/PhysRevB.21.4012

M3 - Article

AN - SCOPUS:0000732416

VL - 21

SP - 4012

EP - 4016

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 9

ER -