Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1998-01-08
Physics
Condensed Matter
Disordered Systems and Neural Networks
29 pages, Revtex file, 2 figures included, submitted to `Phys. Rev. B'
Scientific paper
We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as an annealed spin variable, thereby avoiding the usual average over the random field distribution. This allows to study the influence of the distribution on the phase diagram in finite dimensions. The thermodynamics and the correlation functions are obtained as solutions of a set a coupled partial differential equations with magnetization, temperature and disorder strength as independent variables. A preliminary analysis based on high-temperature and 1/d series expansions shows that the theory can predict accurately the dependence of the critical temperature on disorder strength for dimensions d>4. For the bimodal distribution, we find a tricritical point which moves to weaker fields as the dimension is reduced. For the Gaussian distribution, a tricritical point may appear for d slightly above 4.
Kierlik Edouard
Rosinberg Martin Luc
Tarjus Gilles
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