Geodesic
The Spectrum of Two-Particle Bound States for the Transfer Matrices of Gibbs Fields (an Isolated Bound State)
Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 3, pp. 52-69

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This paper initiates a general study of the spectrum of two-particle bound states of transfer matrices for a fairly wide class of Gibbs fields at high temperature $T$. In the present first part of this study, a detailed statement of the problem is given and the existence of a so-called “isolated level” lying at a distance $\sim 1/{T^2}$ from the boundary of the continuous spectrum is established for all values of the total quasimomentum $\Lambda$ of the system. In the concluding part of the paper, we prove that there are no other bound states provided that $\Lambda$ is far from certain singular values. In the second part, we will consider bound states for $\Lambda$ close to the singular values. The distance from these states (adjacent levels, in the authors' terminology) to the continuous spectrum is at most of the order of $1/T^4$.
Keywords: Gibbs fields, bound states, Fredholm determinant, generic potential.
Mots-clés : transfer matrix 
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     author = {E. L. Lakshtanov and R. A. Minlos},
     title = {The {Spectrum} of {Two-Particle} {Bound} {States} for the {Transfer} {Matrices} of {Gibbs} {Fields} (an {Isolated} {Bound} {State)}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {52--69},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2004_38_3_a4/}
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E. L. Lakshtanov; R. A. Minlos. The Spectrum of Two-Particle Bound States for the Transfer Matrices of Gibbs Fields (an Isolated Bound State). Funkcionalʹnyj analiz i ego priloženiâ, Tome 38 (2004) no. 3, pp. 52-69. http://geodesic.mathdoc.fr/item/FAA_2004_38_3_a4/