Can there only be a critical temperature if there is some natural unit for an observable in the model, i.e. if there is a natural scale for something? Otherwise I don't see how for a system there could be a rule how the value of $T_c$ gets actually terminated. And do this transitions vanish from the model, if one does a limit where these units get irrelevant?
Is it a priori arbitrary which quantity (lenght, energy, charge,...) has to have the specified unit? And/Or have there to be more such units to make up a critical temperature? Lastly, can there only be a phase transition in a system if there is an associated critical temperature $T_c$?