For Pareto vertex weights, the critical Potts inverse temperature is bounded by simple logarithms of the number of states, with sharpened asymptotics for large and small state counts.
Janssen, The critical temperature in the annealed Potts model with exponential vertex weights, Eurandom preprint series, 2025-08
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Analysis of quantities determining the critical inverse temperature in the annealed Potts model with Pareto vertex weights
For Pareto vertex weights, the critical Potts inverse temperature is bounded by simple logarithms of the number of states, with sharpened asymptotics for large and small state counts.