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The Curie-Weiss model is an exchangeable probability measure $\mu$ on $\{0,1\}^n.$

It has two parameters -- the external magnetic field $h$ and the interaction $J$.

A natural problem is to determine when this measure extends to an exchangeable measure

on $\{0,1\}^{\infty}$. We will discuss two approaches to the following result:

$\mu$ can be (infinitely) extended if and only if $J\geq 0$. One of these

approaches relies on the classical Hausdorff moment problem. When $Jn$ can $\mu$ be extended to an exchangeable measure on $\{0,1\}^l$. Our approach

to this question involves an apparently new type of moment problem, which we will

solve. We then take $J=-c/l$, and determine the values of $c$ for which $l$-extendibility

is possible for all large $l$. This is joint work with Jeff Steif and Balint Toth.