# Mathematics Colloquia and Seminars

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### On the Absence of Ferromagnetism in Typical 2D Ferromagnets

**Mathematical Physics & Probability**

Speaker: | Lincoln Chayes, UCLA |

Location: | 1147 MSB |

Start time: | Tue, Oct 17 2006, 2:10PM |

The Ising ferromagnet in d = 2 is the simplest model of interacting magnetic constituents that exhibits a cooperative phase transition. Ising systems serve not only as models of magnetic materials, there are other phenomenological interpretations related to binary alloys, adsorbed gasses etc. not to mention a host of uses in other areas of science: political distributions, dueling protagonists and so forth. In all cases, the well known phase transition is presumed to teach us something about the collective behaviors in these systems. But for the primary interpretation, other forces must be taken into account, in particular the longrange dipolar interactions. As it turns out, these forces have significant impact on the phase structure of 2D Ising ferromagnets and, as the title indicates, exclude the possibility of ferromagnetism in these systems.