Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-05-27
Phys. Rev. E 78, 021106 (2008)
Physics
Condensed Matter
Statistical Mechanics
12 pages, 10 figures, published version
Scientific paper
10.1103/PhysRevE.78.021106
The spectrum of the Lipkin-Meshkov-Glick model is exactly derived in the thermodynamic limit by means of a spin coherent states formalism. In the first step, a classical analysis allows one to distinguish between four distinct regions in the parameter space according to the nature of the singularities arising in the classical energy surface; these correspond to spectral critical points. The eigenfunctions are then analyzed more precisely in terms of the associated roots of the Majorana polynomial, leading to exact expressions for the density of states in the thermodynamic limit. Finite-size effects are also analyzed, leading in particular to logarithmic corrections near the singularities occuring in the spectrum. Finally, we also compute expectation values of the spin operators in a semi-classical analysis in order to illustrate some subtle effects occuring in one region of the parameter space.
Mosseri Remy
Ribeiro Paul
Vidal Jordi
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