Density of states of continuous and discrete spin models: a case study

Details Density of states of continuous and discrete spin models: a case study Density of states of continuous and discrete spin models: a case study

2011-10-06

arxiv.org/abs/1110.1276v2

Journal of Statistical Mechanics: Theory and Experiment (2012) P02007

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1088/1742-5468/2012/02/P02007

A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (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 the present 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 of the one-dimensional XY model. We also discuss the possible consequences of this result for the general case.

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