## Research Highlight

Posted by h.z. on September 14, 2011

**Partition function loop series.**
In a paper
published in Journal of Physics A, Jing-Qing
Xiao and Haijun Zhou
derived the loop series expressions for the partition function and the
generalized partition functions of a general
graphical model. Besides obtaining the free-energy variationals used by
the
mean-field replica-symmetry-broken spin-glass theory, they obtained
message-passing
equations (belief-propagation and survey-propagation) as necessary and
sufficient conditions to
cancel the
loop corrections of all subgraphs with dangling edges. This paper is
a mathematical approach to the theory of spin-glasses. It helps
to place the RSB spin-glass theory and the message-passing algorithms
on a firmer mathematical ground. For the full paper, see here.