Abstract
We consider the Harmonic crystal, a measure on \(\mathbb{R}^{\mathbb{Z}^{d}}\) with Hamiltonian H(x)=∑i,jJi,j(x(i)−x(j))2+h∑i(x(i)−d(i))2, where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤd. The configuration d is given and considered as observations. The ‘couplings’ Ji,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.
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