BKT-like transition in the Potts model on an inhomogeneous annealed network

TL;DR

This paper demonstrates an inverted BKT phase transition in the ferromagnetic q-state Potts model on an inhomogeneous annealed network, revealing critical behavior and power-law distributions across the phase diagram.

Contribution

It uncovers a novel inverted BKT transition in the Potts model on an annealed network, including for q ≥ 3 where first-order transitions are typical.

Findings

Identifies inverted BKT transition for all q ≥ 1.

Shows power-law distributions of correlations in the normal phase.

Provides temperature dependence of key thermodynamic quantities.

Abstract

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