Abstract
We study the classical statistical mechanics of the plane rotator, and show that there is a unique translation invariant equilibrium state in zero external field, if there is no spontaneous magnetization. Moreover, this state is then extremal in the equilibrium states. In particular there is a unique phase for the two dimensional rotator, and a unique phase for the three dimensional rotator above the critical temperature. It is also shown that there is a unique equilibrium state in a sufficiently large external field.
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References
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Bricmont, J., Fontaine, J., Landau, L. (1978). On the uniqueness of the equilibrium state for plane rotators. In: Dell'Antonio, G., Doplicher, S., Jona-Lasinio, G. (eds) Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08853-9_36
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DOI: https://doi.org/10.1007/3-540-08853-9_36
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