What is the fundamental difference between the Ising and Potts models ...

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What I understand is that the only difference between the Ising and Potts models is that Ising has two types of spins, and Potts has n types of spins. However, I am wondering if the Hamiltonian (energy formula) is the same or different. Are the Hamiltonianas the same or different? What other differences do they have?


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