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Unpublished Paper
Refined Asymptotics of the Finite-Size Magnetization via a New Conditional Limit Theorem for the Spin
(2013)
  • Richard S Ellis, University of Massachusetts - Amherst
  • Jingrah Li
Abstract
We study the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our main theorem generalizes the main result in a previous paper [12] in which the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model is given. In that paper our goal is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume-Capel model. The main result is that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter _ governing the speed at which the sequence approaches criticality is below a certain threshold _0. Our main theorem in the present paper on the fluctuations of the spin per site around the thermodynamic magnetization is based on a new conditional limit theorem for the spin, which is closely related to a new conditional central limit theorem for the spin.
Disciplines
Publication Date
2013
Citation Information
Richard S Ellis and Jingrah Li. "Refined Asymptotics of the Finite-Size Magnetization via a New Conditional Limit Theorem for the Spin" (2013)
Available at: http://works.bepress.com/richard_ellis/48/