Abstract
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Highlights
In our paper we study the asymptotical behavior of the thermal correlation functions in the limit of low temperature provided that the chain is long enough while the number of flipped spins is moderate
The equations (23) and (38) for the form-factors which are the basic quantities in the above correlation functions are shown to be related to the generating functions of self-avoiding random walks and boxed plane partitions
The estimate of the asymptotical behavior of the persistence correlation functions of the operators Πn and Fn is done for low temperatures
Summary
In our paper we study the asymptotical behavior of the thermal correlation functions in the limit of low temperature provided that the chain is long enough while the number of flipped spins is moderate. We will calculate the leading terms of their asymptotics, provided that the characteristic parameters of the system are large enough, including the critical exponents of these correlation functions in the low temperature limit, and the related amplitudes These amplitudes are found to be proportional to the squared numbers of boxed plane partitions. The XX0 model and its solution are presented shortly, the considered correlation functions are defined and the amplitudes of the state vectors are written in terms of Schur functions This representation allows to calculate the form-factors of operators in Section 3 applying the formulas of the Binet-Cauchy type. The proof of the determinantal formulas crucial for this paper is given in Appendix II
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