Critical Behavior of a Compressible Ising Antiferromagnet at Constant Pressure*

The effect of elastic degrees of freedom in Ising models has long been a subject of interest. %Theoretical studies on compressible Ising models were done by Bergman and Halperin\footnote{D. J. Bergman and B. I. Halperin, Phys. Rev. B {\bf 13}, 2145 (1976)}, A review of the theoretical studies was given by D\"unweg\footnote{B. D\"unweg, Habilitationsschrift, MPIP, Mainz, Germany (2000)} who predicts different behaviors for ferromagnetic and antiferromagnetic systems. %and recently by D\"unweg\footnote{B. D\"unweg, Habilitationsschrift, Max-Planck-Institut f{\"u}r Polymerforschung, Mainz, Germany (2000)}. %Using Monte Carlo simulations, Laradji and Landau\footnote{Phys. Rev. B {\bf 51}, 4894 (1995)} %M. Laradji and D. P. Landau, Phys. Rev. B {\bf 51}, 4894 (1995)} %studied the phase behavior of ferromagnet at constant pressure %and their results agree well with the theoretical predictions, %but Tavazza {\em et el.} \footnote{Phys. Rev. B {\bf xx}, xx (2004)} F. Tavazza and D. P. Landau and J. Adler, Phys. Rev. B {\bf xx}, xx (2004)} %found discrepancy with the theory on ferromagnet at constant volume. Numerical results for ferromagnetic Ising models don't always agree with the theoretical predications \footnote{M. Laradji and D. P. Landau, Phys. Rev. B {\bf 51}, 4894 (1995)} \footnote{B. D{\"u}nweg and D. P. Landau, Phys.\ Rev.\ B {\bf 48}, 14182 (1993)} \footnote{F. Tavazza, D. P. Landau and J. Adler, Phys. Rev. B (in press)}, and to further test the theory we present our Monte Carlo simulations of an elastic antiferromagnetic Ising model. Spins interact via a Stillinger-Weber-like potential and data were obtained over a wide range of system sizes (from 512 to 110,592 spins). We find a phase diagram that has a line of 2nd order transitions between ordered and disordered states. Our analysis shows that this transition belongs to the universality class of the rigid 3-D Ising model, but the possibility of a slow crossover toward a first order transition cannot be completely ruled out. We also examine the distributions of interaction constants in the effective Landau-Ginzburg-Wilson Hamiltonian.