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

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Abstract
We present a detailed description of the rich variety of phase transitions exhibited by the continuum Heisenberg model of spin fluid, treated by means of integral equation methods (mean spherical approximation and reference hypenetted chain equation) and simulation techniques (canonical ensemble and Gibbs ensemble Monte Carlo). We focus here on ferromagnetic interactions. An order-disorder transition and a gas-liquid transition are characterized. Both transitions are coupled at low temperature, but near the gas-liquid critical point only ordered states are involved in the gas-liquid transition. Our data preclude the existence of a tricritical point, but there is evidence that the line of Curie points may end up in a critical end point at the gas-liquid spinodal. At low densities there is a strong tendency to clustering, and the system organizes in magnetized droplets. The reference hypernetted chain equation yields a spinodal line (locus of Curie points) for moderate to high densities, whereas at low densities the equation breaks down at a singularity with the characteristic behavior of a square root branch point.