Abstract
We present the formulation of the Replica Ornstein-Zernike equations for a model of positionally frozen disordered Heisenberg spin system. The results are obtained for various models, one in which the particle positions correspond to a frozen hard sphere fluid, another system in which the configurations are generated by a random insertion of hard spheres, a system of randomly distributed spins, and finally a system corresponding to a soft sphere fluid quenched at high and low temperatures. We will see that the orientational structure of the spin system is fairly well reproduced by the integral equation which, however, does not correctly account for the critical behaviour.
Highlights
The study of positionally frozen dipolar fluids has been the focus of various works in recent years [1,2,3,4], using both simulation techniques [1,3], mean field theory [2] and quite recently the Replica Ornstein-Zernike (ROZ) integral equation theory [4]
In related works [5,6], the authors focused on the ferromagnetic transition of a positionally frozen Heisenberg spin system, which is amenable to be treated more accurately using simulation techniques adapted for near critical conditions
In this paper we will explore the capabilities of the ROZ integral equation treatment to describe the ferromagnetic transition in positionally frozen Heisenberg systems
Summary
The study of positionally frozen dipolar fluids has been the focus of various works in recent years [1,2,3,4], using both simulation techniques [1,3], mean field theory [2] and quite recently the Replica Ornstein-Zernike (ROZ) integral equation theory [4]. For this purpose we will solve the ROZ equations in the Hypernetted Chain (HNC) approximation for the models simulated in references [5] and [6], namely, Heisenberg spin systems in which the spin positions are frozen according to the configurations of hard sphere (HS) fluids (model A) [5], a random distribution of spins (model B) [5], and soft spheres (SS) quenched at high and low temperatures (models C and D, respectively) [6].
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