Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on \(\mathbb{R}^{\mathbb{Z}^{d}}\) with Hamiltonian \(H(\x)=\sum_{i,j}J_{i,j}(\x(i)-\x(j))^{2}+ h\sum_{i}(\x(i)-\dd(i))^{2}\), where \(\x, \dd\) are configurations, \(\x(i),\dd(i)\in\mathbb{R}\), \(i,j\in{\mathbb{Z}^{d}}\). The configuration \(\dd\) is giv...

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Bibliographic Details
Published in:arXiv.org 2007-06
Main Authors: Ferrari, Pablo A, Niederhauser, Beat M, Pechersky, Eugene A
Format: Article
Language:English
Subjects:
Configurations
Couplings
Online Access:Get full text
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Summary:We consider the Harmonic crystal, a measure on \(\mathbb{R}^{\mathbb{Z}^{d}}\) with Hamiltonian \(H(\x)=\sum_{i,j}J_{i,j}(\x(i)-\x(j))^{2}+ h\sum_{i}(\x(i)-\dd(i))^{2}\), where \(\x, \dd\) are configurations, \(\x(i),\dd(i)\in\mathbb{R}\), \(i,j\in{\mathbb{Z}^{d}}\). The configuration \(\dd\) is given and considered as observations. The `couplings' \(J_{i,j}\) are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration \(\m\) corresponding to the Hamiltonian.
ISSN:2331-8422