The Relation Between KMS-states for Different Temperatures

Christian D. Jäkel
March 30, 1998
Given a thermal field theory for some temperature $\beta^{-1}$, we construct the theory at an arbitrary temperature $ 1 / \beta'$. Our work is based on a construction invented by Buchholz and Junglas, which we adapt to thermal field theories. In a first step we construct states which closely resemble KMS states for the new temperature in a local region $\mathcal{O}_\circ \subset \mathbb{R}^4$, but coincide with the given KMS state in the space-like complement of a slightly larger region $\hat{\mathcal{O}}$. By a weak*-compactness argument there always exists a convergent subnet of states as the size of $\mathcal{O}_\circ$ and $ \hat{\mathcal{O}}$ tends towards $ \mathbb{R}^4$. Whether or not such a limit state is a global KMS state for the new temperature, depends on the surface energy contained in the layer in between the boundaries of $ \mathcal{O}_\circ$ and $ \hat{\mathcal{O}}$. We show that this surface energy can be controlled by a generalized cluster condition.
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Keywords: 
cluster condition, thermal states