Phase diagram in a continuum model of the classical Heisenberg ferromagnet: mean spherical approximation

An Integral Equation Approach to Orientational Phase Transitions in Two and Three Dimensional Disordered Systems

“…In the limiting case of α → 0, the RZH closure simply reproduces the MSA closure. The usual approach for orientation-dependent functions such as γ(r, ω 1 , ω 2 ) is to expand in spherical harmonics as both Sokolovska [17] and Perera [23] did, leading to the appearance of matrix terms of the form…”

“…(or A klµ in the notation of Klapp and Patey [25] and Y klµ in Sokolovska's work [17]) once the OZ equation is decoupled into its components. These terms appear both in the equation itself and in the expressions to evaluate thermodynamic properties.…”

“…It is well known that the spontaneous symmetry breaking associated with the ferromagnetic transition gives rise to transverse fluctuations, known as Goldstone modes, which reflect in a divergence of the transverse magnetic susceptibility. It has been proved that Lovett's equation automatically reproduces the presence of Goldstone modes in orientationally ordered phases [17,23,21], but this is not evident when the BG equation is used. In fact, we have found that the MSA transverse magnetic susceptibility remains finite in the ferromagnetic phases at zero field, whereas the RHNC equation breaks down at small but finite fields, signalling the presence of a divergence.…”

“…Particularly, renewed effort has been devoted to devise solution methods for the inhomogeneous Ornstein-Zernike equation [7], being evident that the classical isotropic homogeneous integral equation approaches could never throw light into the problem of the structured phases despite its ability to delimit the boundaries of stability in various relevant systems, such as the dipolar hard sphere fluid [8,9] and the ferromagnetic [10] and antiferromagnetic Heisenberg spin fluid [11]. Computer simulation [12][13][14][15] and density functional theory [12,16] were for some time the only available alternative to study the thermodynamics and structure of the orientationally ordered phases, until Sokolovska [17] presented the solution of the Mean Spherical Approximation (MSA) for the continuum ferromagnetic phase of the Heisenberg spin fluid, using Lovett's equation [18] to relate the one and two body correlation functions. Independently, Lado and Lomba [19] solved a reference Zerah-Hansen approximation for the same system, but using the Born-Green equation to connect one and two-body density correlations.…”

Monte Carlo Simulation of Phase Equilibria in Ising Fluids and Their Mixtures

“…The importance of such models lies in their display of a rich variety of transitions between solid, liquid, and gas, as well as magnetically ordered and disordered phases, which may occur in real systems. The liquid-gas and magnetic para-ferro phase transitions in spin fluids were previously studied using the mean field theory [4][5][6], the method of integral equations [7][8][9][10][11], and Monte Carlo (MC) simulation techniques [2,7,10,[12][13][14][15].…”