Abstract
In this work, we provide exact solutions for the ideal boson lattice gas on the infinitely ramified star and wheel graphs. Within a tight-binding description, we show that Bose-Einstein condensation (BEC) takes place at a finite temperature after a proper rescaling of the hoping integral ɛ connecting a central site to the peripheral ones. Analytical expressions for the transition temperature, the condensed gas fraction, and the specific heat are given for the star graph as a function of the density of particles n. In particular, the specific heat has a mean-field character, being null in the high-temperature noncondensed phase with a discontinuity at T(c). In the wheel graph, on which the peripheral sites form a closed chain with hopping integral t, BEC takes place only above a critical value of the ratio ɛ/t for which a gap ΔE appears between the ground state and a one-dimensional band. A detailed analysis of the BEC characteristics as a function of n and ΔE is provided. The specific heat in the high-temperature phase of the wheel graph remains finite due to correlations among the peripheral sites.
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