# The Relation Between KMS States For Different Temperatures

C. Jaekel
Published 1998 · Physics, Mathematics

Abstract. 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 Ô. By a weak*-compactness argument there always exists a convergent subnet of states as the size of $$\mathcal O_{\circ}$$ and Ô 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 Ô. We show that this surface energy can be controlled by a generalized cluster condition.
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