Spherical Model in a Random Field |
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Authors: | A E Patrick |
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Institution: | (1) Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia |
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Abstract: | We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field.
We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it
self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations
of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores
the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate
the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of
the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼r
4−d
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Keywords: | Critical fluctuations Disordered spin systems Gibbs states Self-averaging |
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