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arXiv · 1203.5808

Random Field Induced Order in Low Dimension

Nicholas Crawford
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Abstract

Consider the behavior of a classical O(n) model in a weak random external field acting along some $k$-dimensional subspace in $\R^n$ 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 $k\leq n-1$ and $d\geq 2$ we show in general that the magnitude of spin projections onto this subspace are small.

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Nicholas Crawford. 2012-10-22. Random Field Induced Order in Low Dimension. https://doi.org/10.1209/0295-5075%2F102%2F36003

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