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The condition of quasiperiodicity in imaginary time as a constraint at the functional integration and the time-dependent \(ZZ\)-correlator of the \(XX\) Heisenberg magnet. (Russian. English summary) Zbl 1083.82014

Zap. Nauchn. Semin. POMI 317, 142-173 (2004); translation in J. Math. Sci., New York 136, No. 1, 3607-3624 (2006).
The paper is a continuation of the previous results of the author [see K. Malyshev, Theor. Math. Phys. 136, No. 2, 1143–1154 (2003); translation from Teor. Mat. Fiz. 136, No. 2, 285–298 (2003), C. V. Benton (ed.), New developments in mathematical physics research, Nova Sci. Publ. Hauppauge, NY, 85–116 (2004)]. Here in section 2 a functional integration approach for the calculation of the longitudinal correlation functions of the \(XY\) Heisenberg magnet in the constant homogeneous field is considered. In section 3 a procedure is explained which allows to compute the square root of the determinants, and it demonstrates the coincidence of the results of the 2004 paper cited above for generating functionals, namely the generating functionals of the correlators are defined in the form of the functional integrals over anti-commuting variables. In section 4 for the \(XX\) Heisenberg magnet an application of the approach is given in the case of the two-point correlator of third components of spins with an explicit dependence on time.

MSC:

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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