A self-consistent Ornstein-Zernike approximation for the Random Field Ising model

Abstract

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.

29 pages, Revtex file, 2 figures included, submitted to `Phys. Rev. B'

References in corpus (4)

• Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?
• Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach
• The 3-d Random Field Ising Model at zero temperature
• Scaling of the Random-Field Ising Model at Zero Temperature

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• Hierarchical Reference Theory of critical fluids in disordered porous media
• A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0