# (1974). "Equilibrium states of thin energy shells." Memoirs of the American Mathematical Society 150.

# (1974). "Equilibrium states of thin energy shells." *Memoirs of the American Mathematical Society* 150.

*Memoirs of the American Mathematical Society*, 1974, Number 150

"In recent papers Lanford, Ruelle, and Dobrushin have used the grand canonical ensemble of statistical mechanics on a finite lattice to define and analyze equilibrium states for distribution of particles on the infinite lattice, Z^{n}. These have been named Gibb's states. In this paper we consider the probability measures on configurations of particles in a finite lattice obtained by restricting the grand canonical ensemble to an energy shell, or set of particle configuration which share a common total energy with respect to a vector of potentials. The set of weak limits of those measures as the finite lattice expands to Z^{n} is used to define a class ... of translation invariant states on Z^{n}. this class of states is convex and it is shown that the extreme points of the class are Gibbs' states...."

The American Mathematical Society published Thompson's dissertation as part of a *Memoirs of the AMS* series. AMS journals are noted for "the highest quality in mathematical research ... covering a broad range of mathematics. Each journal is managed by editors who are prominent in their fields."

For more information on this edition of the journal, please see: www.ams.org/books/memo/0150/

Thompson wrote in 1992 that his "dissertation deals with statistical mechanics, a branch of theoretical physics. For the fun of it, note the Mahamantra on the acknowledgments page. Srila Prabhupada later said in 1975, 'So it is very nice. You have dedicated to Hare Krsna.'"