Thermodynamics and phase transitions in the Overhauser model

G. Fano

Valdir C. Aguilera-Navarro, MANUEL DE LLANO, Stella M. Peltier +1 more

Two infinite families of two-parameter generalized Overhauser orbitals are introduced and shown to satisfy explicitly, for occupied states, the self-consistent Hartree-Fock equations in the thermodynamic limit. For an attractive $\ensuremath{\delta}$ interaction, they give lower Hartree-Fock energy than the usual plane-wave solutions, even for relatively weak coupling and/or low density. The limiting members (possessing an infinite number of harmonics) of both families appear to tend to a "classical static lattice" state, via a second-order transition for one family and via first order for the other. The related density profiles and energy expressions are calculated as functions of the two new parameters. A direct variation with respect to these parameters was done numerically and results are presented graphically.

M. Broidioi, Bruno Nachtergaele, André F. Verbeure

A Goldstone-type theorem is derived to reveal the nature of the spontaneous symmetry breaking occurring in the Overhauser model. Explicit expressions for the equilibrium states of the model are calculated. The fluctuations of the fields satisfy a central limit theorem. The limit is a new set of Fermionic fields that inherit their dynamics from the original model. In the low-temperature phase, where the order parameter does not vanish, this dynamics is nontrivial and basically shows oscillations with a frequency related to the order parameter.

Malte Henkel, Haye Hinrichsen, Sven Lübeck

G. Toulouse

Luca Angelani, Giancarlo Ruocco

The thermodynamics and topology of mean-field models with 2+k body interaction terms (generalizing XY model) are derived. Focusing on two particular cases (2+4 and 2+6 body interaction terms), a comparison between thermodynamic (phase transition energy, thermodynamically forbidden energy regions) and topological (singularity and curvature of saddle entropy) properties is performed. We find that (i) a topological change is present at the phase transition energy; however, (ii) only one topological change occurs, also for those models exhibiting two phase transitions; (iii) the order of a phase transition is not completely signaled by the curvature of topological quantities.