Geodesic
Statistical mechanics of a paramagnetic chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 2, pp. 286-300 Cet article a éte moissonné depuis la source Math-Net.Ru

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The transfer matrix method is used to find the exact partitiorJ function in the thermodynamic limit of a two-level system coupled to a one-dimensional elastic, cyclically closed chain of atoms. The number of two-level objects ($\dfrac12$ spins) is equal to the number of degrees of freedom of the chain (the number of modes). The spin system is in a transverse field $\omega_0$, and the chain in a linear potential $\alpha\varphi^2$. The following results are obtained. At $\omega_0=0$, the problem is equivalent to the one-dimensional Kac model with antiferromagnetic exchange interaction between the spins. There is no phase transition in the system at any $\omega_0$ in contrast to the case with a finite number of field modes. The interaction of the spins with the lattice suppresses the Curie paramagnetism, and in the limit $T\to0$ the transverse susceptibility of the system remains finite. 
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     author = {A. F. Sadreev},
     title = {Statistical mechanics of a~paramagnetic chain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {1982},
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     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_50_2_a9/}
}
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A. F. Sadreev. Statistical mechanics of a paramagnetic chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 2, pp. 286-300. http://geodesic.mathdoc.fr/item/TMF_1982_50_2_a9/

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