Mathematics Session O Room : 111

The partition function of the Potts model can be expressed in terms of famous combinatorial graph polynomials for restricted Hamiltonians. We investigate the Hamiltonian with variable edge interaction and external magnetic field, for which the partition function is the V-polynomial. Because the partition function is a polynomial, we can use motivic methods from algebraic geometry to characterize the complexity of the partition function. We also characterize the computational complexity of the partition function and determine that the zeros of the partition function are not polynomial countable. Future work includes providing conditions for when the partition function uniquely determines the underlying graph of the Potts model.