Abstract
We propose a way to study one-dimensional statistical mechanics models with complex-valued action using transfer operators. The argument consists of two steps. First, the contour of integration is deformed so that the associated transfer operator is a perturbation of a normal one. Then the transfer operator is studied using methods of semi-classical analysis. In this paper, we concentrate on the second step, the main technical result being a semi-classical estimate for powers of an integral operator which is approximately normal.
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Communicated by Jens Marklof.
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Disertori, M., Sodin, S. Semi-Classical Analysis of Non-Self-Adjoint Transfer Matrices in Statistical Mechanics I. Ann. Henri Poincaré 17, 437–458 (2016). https://doi.org/10.1007/s00023-015-0397-x
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DOI: https://doi.org/10.1007/s00023-015-0397-x