Random Field Induced Order in Low Dimension

2012/03/31 by Nicholas Crawford · 1 citation
Mathematics · Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:60-XX #msc:82-XX

paper · pdf · doi:10.1209/0295-5075/102/36003

5 pages. Summary of forthcoming work

arxiv created 2012/10/22 · arxiv updated 2015/06/04

Abstract

Consider the behavior of a classical O(n) model in a weak random external field acting along some k-dimensional subspace in \Rⁿ with k<n. We show rigorously that if k=n-1, for the model defined on \Z^d, d =2, 3 there is residual magnetic order perpendicular to the subspace which supports the distribution of the random field only. Furthermore, when k≤ n-1 and d≥ 2 we show in general that the magnitude of spin projections onto this subspace are small.

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