# Mathematics Colloquia and Seminars

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### From Classical to Quantum Interfaces

**Mathematical Physics & Probability**

Speaker: | Alain Messager, Centre de Physique Theorique, Luminy |

Location: | 2112 MSB |

Start time: | Thu, Apr 27 2006, 3:10PM |

Interfaces between different phases play a major role in statistical mechanics (e.g., the shape of crystals). One of the main questions is to determine whether an interface is rigid or not at low temperatures. In the classical case a typical result is that interfaces in two-dimensioanl models, such as the Ising model, are rough (e.g., they behave as Brownian motion). On the other hand, in the Ising model on Z3 the interface in the 100 direction is rigid. Quantum interfaces are more complicated since the possible ground states may form a continuous family. instead of a finite set of configurations. I will explain the situation for the anisotropic Heisenberg model in three dimensions where a rigid quantum interface appears.