# Mathematics Colloquia and Seminars

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### Droplet Energies in the XXZ Model

**Mathematical Physics & Probability**

Speaker: | Shannon Starr, UCLA |

Location: | 693 Kerr |

Start time: | Tue, May 31 2005, 3:10PM |

For the kink XXZ model in one-dimension, and with spins 1/2, it has been recently proved that there is ferromagnetic ordering of energy levels. This means the following. Let E_L(n) be the lowest energy among all eigenvectors whose total spin is L/2-n. Then E_L(n) is increasing with n. An interesting question is to try to find a formula for E_L(n) in the limit that L goes to infinity. I will show how to do this, using the Bethe ansatz and the Perron Frobenius theorem. It turns out that the lowest eigenvectors are well-described as droplets. This is joint work with Bruno Nachtergaele and Wolfgang Spitzer