Abstract
We consider a mean-field continuum model of classical particles in R d with Ising or Heisenberg spins. The interaction has two ingredients, a ferromagnetic spin coupling and a spin-independent molecular force. We show that a feedback between these forces gives rise to a first-order phase transition with simultaneous jumps of particle density and magnetization per particle, either at the threshold of ferromagnetic order or within the ferromagnetic region. If the direct particle interaction alone already implies a phase transition, then the additional spin coupling leads to an even richer phase diagram containing triple (or higher order) points.
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REFERENCES
N. Angelescu and V. A. Zagrebnov, A generalized quasiaverage approach to the description of the limit states of the n-vector Curie-Weiss ferromagnet, J. Stat. Phys. 41:323–334 (1985).
P. Ballone, Ph. de Smedt, J. L. Lebowitz, J. Talbot, and E. Waisman, Computer simulation of a classical fluid with internal quantum states, Phys. Rev. A 35:942–944 (1987).
T. Burke, J. L. Lebowitz, and E. Lieb, Phase transition in a model quantum system: Quantum corrections to the location of the critical point, Phys. Rev. 149:118–122 (1966).
L. Chayes, S. B. Sholsman, and V. A. Zagrebnov, Discontinuity of the magnetization in diluted O(n)-model. Preprint (CPT, Luminy, Marseille, 1998).
I. Csiszár, Sanov property, generalized I-projection and a conditional limit theorem, Ann. Prob. 12:768–798 (1984).
D. J. Gates and O. Penrose, The van der Waals limit for classical systems. I: A variational principle, Commun. Math. Phys. 15:255–276 (1969).
P. G. de Gennes, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1974).
H. O. Georgii, Gibbs Measures and Phase Transitions, De Gruyter Studies in Mathematics, Vol. 9 (de Gruyter, Berlin, 1988).
H. O. Georgii and O. Häggström, Phase transition in continuum Potts models, Commun. Math. Phys. 181:507–528 (1996).
H. O. Georgii and H. Zessin, Large deviations and the maximum entropy principle for marked point random fields, Probab. Theory Relat. Fields 96:177–204 (1993).
B. Groh and S. Dietrich, Spatial structure of dipolar ferromagnetic liquids, Phys. Rev. Lett. 79:749–752 (1997).
Ch. Gruber and R. B. Griffiths, Phase transition in a ferromagnetic fluid, Physica A 138:220–230 (1986).
P. C. Hemmer and D. Imbro, Ferromagnetic fluids, Phys. Rev. A 16:380–386 (1977).
K. Johansson, On separation of phases in one-dimensional gases, Commun. Math. Phys. 169:521–561 (1995).
J. L. Lebowitz and O. Penrose, Rigorous treatment of the Van der Waals Maxwell theory of the liquid vapour transition, J. Math. Phys. 7:98–113 (1966).
J. L. Lebowitz, A. E. Mazel, and E. Presutti, Liquid-vapor phase transitions for systems with finite range interactions, J. Stat. Phys. (to appear, 1998).
E. Lieb, Quantum-mechanical extension of the Lebowitz-Penrose theorem on the Van der Waals theory. J. Math. Phys. 7:1016–1024 (1966).
E. Lomba, J.-J. Weis, N. G. Almarza, F. Bresme, and G. Stell, Phase transitions in a continuum model of the classical Heisenberg magnet: The ferromagnetic system, Phys. Rev. E 49:5169–5178 (1994).
D. C. Mattis, The Theory of Magnetism (Harper & Row, New York, 1965).
S. A. Pikin, Structural Transformations in Liquid Crystals (in Russian) (Moscow, Nauka, 1981).
R. T. Rockafellar, Convex Analysis (Princeton University Press, Princeton, N.J., 1970).
D. Ruelle, Existence of a phase transition in a continuous classical system, Phys. Rev. Lett. 27:1040–1041 (1971).
B. Simon, The Statistical Mechanics of Lattice Gases, Vol. 1 (Princeton University Press, Princeton, N.J., 1993).
K. Sano and M. Doi, Theory of agglomeration of ferromagnetic particles in magnetic fluids, J. Phys. Soc. Japan 52:2810–2815 (1983).
Ph. de Smedt, P. Nielaba, J. L. Lebowitz, J. Talbot, and L. Dooms, Static and dynamic correlations in fluids with internal quantum states: Computer simulations and theory, Phys. Rev. A 38:1381–1394 (1988).
M. J. Stevens and G. S. Grest, Structure of soft-sphere dipolar fluids, Phys. Rev. E 51:5962–5975 (1995).
M. J. Stevens and G. S. Grest, Phase coexistence of a Stockmayer fluid in an applied field, Phys. Rev. E 51:5976–5983 (1995).
J.-J. Weis, M. J. P. Nijmeijer, J. M. Taveres, and M. M. Telo de Gama, Phase diagram of Sleisenberg fluids: Computer simulation and density functional theory, Phys. Rev. E 51:5962–5975 (1997).
B. Widom and J. S. Rowlinson, New model for the study of liquid-vapor phase transition, J. Chem. Phys. 52:1670–1684 (1970).
V. A. Zagrebnov, Long-range order in a lattice-gas model of nematic liquid crystals, Physica A 232:737–746 (1996).
H. Zhang and M. Widom, Global phase diagrams for dipolar fluids, Phys. Rev. E 49:R3591–R3593 (1994).
Zhu Yun, E. Haddadian, T. Mou, M. Gross, and Jing Liu, Rôle of nucleation in the structure evolution of a magnetorheological fluid, Phys. Rev. E 53:1753–1759 (1996).
A. Yu. Zubarev and A. O. Ivanov, Kinetics of a magnetic fluid phase separation induced by an external magnetic field, Phys. Rev. E 55:7192–7202 (1997).
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Georgii, HO., Zagrebnov, V. On the Interplay of Magnetic and Molecular Forces in Curie–Weiss Ferrofluid Models. Journal of Statistical Physics 93, 79–107 (1998). https://doi.org/10.1023/B:JOSS.0000026728.01594.18
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DOI: https://doi.org/10.1023/B:JOSS.0000026728.01594.18