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We solve the ferromagnetic q-state Potts model on an inhomogeneous annealednetwork which mimics a random recursive graph. We find that this system has theinverted Berezinskii--Kosterlitz--Thouless (BKT) phase transition for any $q\geq 1$, including the values $q \geq 3$, where the Potts model normally showsa first order phase transition. We obtain the temperature dependences of theorder parameter, specific heat, and susceptibility demonstrating featurestypical for the BKT transition. We show that in the entire normal phase, boththe distribution of a linear response to an applied local field and thedistribution of spin-spin correlations have a critical, i.e. power-law, form.Comment: 7 pages, 3 figure

Berezinskii-Kosterlitz-Thouless-like transition in the Potts model on an inhomogeneous annealed network