# Mathematics Colloquia and Seminars

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### Properties of non-translation invariant states for the XXZ model

**Mathematical Physics & Probability**

Speaker: | Shannon Starr, UC Davis |

Location: | 693 Kerr |

Start time: | Tue, Mar 13 2001, 4:10PM |

The ferromagnetic XXZ model admits infinite-volume ground states with broken translation symmetry. This is important because natural ferromagnets also have broken translation symmetry. For my thesis work, I studied the lowest excitations of these ground states. In this talk I will descibe three results: 1) The rate of vanishing for the spectral gap above the (1,1,1)-interface state in 3 dimensions, 2) The lowest excitations of the infinite-volume all-up-spin state in 1d are "droplets", 3) There is a nonvanishing spectral gap above ground state for the spin-S chain for all S, although it is not what you might expect from the spin-1/2 result.