Spherical Model in a Random Field

Details Spherical Model in a Random Field Spherical Model in a Random Field

2007-09-22

arxiv.org/abs/0709.3579v1

Journal of Statistical Physics, vol. 128, No. 5, September 2007, pp. 1211-1235

Physics

Condensed Matter

Statistical Mechanics

29 pages

Scientific paper

10.1007/s10955-007-9353-6

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 $\sim r^{4-d}$.

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