## Abstract

We consider a continuous model for transverse magnetization of spins diffusing in a homogeneous Gaussian random longitudinal field {XV (x); x ∈ ℝ^{d}}, where λ is the coupling constant giving the intensity of the random field. In this setting, the transverse magnetization is given by the formula M(t) = double-struck E signexp{-λ^{2}∫^{t}_{0} ∫^{t}_{0} K(B_{r} - B_{s}) dsdr}, where {B_{t}; t ≥ 0} is the standard process of Brownian motion and K(x) is the covariance function of the original random field V(x). We use large deviation techniques to show that the limit S(λ) = lim_{t→∞} 1/t In M (t) exists. We also determine the small λ behavior of the rate S(λ) and show that it is indeed decaying as conjectured in the physics literature.

Original language | English (US) |
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Pages (from-to) | 233-247 |

Number of pages | 15 |

Journal | Probability Theory and Related Fields |

Volume | 106 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1996 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty