- 98-552 Bach V., Jecko T., Sjoestrand J.
- Correlation Asymptotics of Classical Lattice Spin Systems with Nonconvex Hamilton Function at Low Temperature.
Aug 4, 98
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Abstract. The present paper continues Sj\"ostrand's study
of correlation functions of lattice field theories by means of
Witten's deformed Laplacian. Under the assumptions specified in
the paper and for sufficiently low temperature, we derive an estimate
for the spectral gap of a certain
Witten Laplacian which enables us to prove the exponential decay
of the two-point correlation function and, further, to derive
its asymptotics, as the distance between the spin sites becomes large.
Typically, our assumptions do not require uniform strict convexity and
apply to Hamiltonian functions which
have a single, nondegenerate minimum and no other extremal point.