Mathematics Colloquia and Seminars

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I introduce the class of single species PVBS models defined on a finite, connected subset of Z^d. I will give the finite volume ground states, and show that the dimension of the weak-* infinite volume ground state space depends on the model parameters and the geometry of the infinite volume. Furthermore, I will show that the existence of the spectral gap in the thermodynamic limit depends on the model parameters and the geometry of the infinite volume to which we take the limit.