Critical temperature of non-interacting Bose gases on disordered lattices

TL;DR

This paper analyzes how disorder affects the critical temperature of non-interacting Bose gases on lattices, revealing dependence on dimensionality and filling, with specific results for infinite-range models and three-dimensional systems.

Contribution

It provides a detailed computation of the critical temperature shift due to disorder in lattice Bose gases, including analytical and numerical results across different dimensions.

Findings

Negative critical temperature shift in infinite-range models

Disorder enhances Tc at large filling in 3D

Tc decreases at small filling, consistent with continuum results

Abstract

For a non-interacting Bose gas on a lattice we compute the shift of the critical temperature for condensation when random-bond and onsite disorder are present. We evidence that the shift depends on the space dimensionality D and the filling fraction f. For D -> infinity (infinite-range model), using results from the theory of random matrices, we show that the shift of the critical temperature is negative, depends on f, and vanishes only for large f. The connections with analogous results obtained for the spherical model are discussed. For D=3 we find that, for large f, the critical temperature Tc is enhanced by disorder and that the relative shift does not sensibly depend on f; at variance, for small f, Tc decreases in agreement with the results obtained for a Bose gas in the continuum. We also provide numerical estimates for the shift of the critical temperature due to disorder induced on a non-interacting Bose gas by a bichromatic incommensurate potential.