Phase transitions in a continuum model of the classical Heisenberg magnet: The antiferromagnetic system

We model an antiferromagnetic fluid by a system of hard spheres with embedded classical Heisenberg spins with antiferromagnetic coupling constants. In this system we find from Monte Carlo simulation strong evidence of an order-disorder transition between paramagnetic and antiferromagnetic spatially disordered states, which also appears in an appropriate integral equation theory (reference hypernetted chain). We do not find direct simulation evidence of the presence of gas-liquid coexistence, but find such coexistence via the mean spherical approximation internal energy, which predicts a first-order gas-liquid transition. Analysis of the mean spherical results provides a tentative scenario concerning the way the line of N\'eel transitions approaches a liquid-gas coexistence curve.