Geodesic
Free energy in a one-dimensional spherical model with oscillating potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 406-415 Cet article a éte moissonné depuis la source Math-Net.Ru

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One-dimensional spherical model with slowly decreasing and oscillating potential of the form $\rho(r)=r^{-1}\sin\alpha r$ is considered. The dependence of the free energy upon the boundary conditions is studied. It turns out that in the case of zero (finite, in general) boundary conditions the free energy $\psi_0(\beta)$ is analytical for all $\beta>0$. In the case of periodical boundary conditions the free energy $\psi(\beta)$ coincides with $\psi_0(\beta)$ for small $\beta$'s. However at some points $\beta_c$ the new branches of the free energy arise. Therefore in this situation the standard method of analytical continuation from the domain of small $\beta$'s is not applicable so far as it does not catch the phase transition. 
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     author = {L. V. Bogachev},
     title = {Free energy in~a~one-dimensional spherical model with oscillating potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {406--415},
     year = {1980},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a10/}
}
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L. V. Bogachev. Free energy in a one-dimensional spherical model with oscillating potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 3, pp. 406-415. http://geodesic.mathdoc.fr/item/TMF_1980_42_3_a10/

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