Spin Correlations near the Percolation Concentration in Two Dimensions

R. J. Birgeneau; R. A. Cowley; G. Shirane; H. J. Guggenheim

doi:10.1103/PhysRevLett.37.940

Spin Correlations near the Percolation Concentration in Two Dimensions

R. J. Birgeneau, R. A. Cowley, G. Shirane, and H. J. Guggenheim

Phys. Rev. Lett. 37, 940 – Published 4 October 1976

Abstract

Neutron scattering measurements in the dilute antiferromagnets ${Rb}_{2} {Mn}_{c} {Mg}_{1 - c} F_{4}$ with $c = 0.54 and 0.57$ are presented; for this system the percolation limit is $c_{p} = 0.59$ . Two-dimensional critical scattering is observed with inverse width $ξ$ and amplitude $χ T$ which diverge as a function of $\frac{1}{T}$ ; the divergences cut off when $ξ$ exceeds the size of the larger clusters. A simple self-avoiding walk model accounts well for the observed $ξ$ vs $T$ behavior.

Received 23 June 1976

DOI:https://doi.org/10.1103/PhysRevLett.37.940

Authors & Affiliations

R. J. Birgeneau^†,‡, R. A. Cowley^*,†,‡, G. Shirane^†,‡, and H. J. Guggenheim^†,‡

Massachusetts Institute of Technology, Cambridge, Massachusetts 02139,
Brookhaven National Laboratory, Upton, New York 11973,
Bell Laboratories, Murray Hill, New Jersey 07974

^*Permanent address: Department of Physics, University of Edinburgh, Edinburg, Scotland (now returned).
^†Work at Massachusetts Institute of Technology supported by the National Science Foundation Materials Research Laboratory Grant No. DMR12-03027-ADS.
^‡Work at Brookhaven National Laboratory performed under the auspices of the U. S. Energy Research and Development Administration.