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Density of states of continuous and discrete spin models: a case study. (English) Zbl 1456.82021

Summary: A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti et al. “Microcanonical relation between continuous and discrete spin models”, Phys. Rev. Lett. 106, Article ID 057208, 4 p. (2011)]. Such a relation, inspired by an energy landscape analysis, implies that the density of states of an O(n) spin model on a lattice can be effectively approximated, at least close to the phase transition, in terms of the density of states of an Ising model defined on the same lattice and with the same interactions. In this paper we show that such a relation exactly holds, albeit in a slightly modified form, in the special cases of the mean-field XY model and the one-dimensional XY model. We also discuss the possible consequences of this result for the general case.

MSC:

82B05 Classical equilibrium statistical mechanics (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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