Picture of athlete cycling

Open Access research with a real impact on health...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by Strathclyde researchers, including by researchers from the Physical Activity for Health Group based within the School of Psychological Sciences & Health. Research here seeks to better understand how and why physical activity improves health, gain a better understanding of the amount, intensity, and type of physical activity needed for health benefits, and evaluate the effect of interventions to promote physical activity.

Explore open research content by Physical Activity for Health...

Fluctuations of the local magnetic field in frustrated mean-field Ising models

Dukes, W.M.B. and Dorlas, Tony (2004) Fluctuations of the local magnetic field in frustrated mean-field Ising models. Markov Processes and Related Fields, 10 (4). pp. 585-606. ISSN 1024-2953

Full text not available in this repository. Request a copy from the Strathclyde author

Abstract

We consider fluctuations of the local magnetic field in frustrated mean-field Ising models. Frustration can come about due to randomness of the interaction as in the Sherrington - Kirkpatrick model, or through fixed interaction parameters but with varying signs. We consider central limit theorems for the fluctuation of the local magnetic field values w.r.t. the a priori spin distribution for both types of models. We show that, in the case of the Sherrington - Kirkpatrick model there is a central limit theorem for the local magnetic field, a.s. with respect to the randomness. On the other hand, we show that, in the case of non-random frustrated models, there is no central limit theorem for the distribution of the values of the local field, but that the probability distribution of this distribution does converge. We compute the moments of this probability distribution on the space of measures and show in particular that it is not Gaussian.