Some remarks on the ground state of infinite systems in statistical mechanics

André M. C. Souza

Rudolph Haag

Nicolaas Marinus Hugenholtz

Infinite systems, particularly infinite quantum systems are considered. It is pointed out that algebraic methods can be applied not only to statistical mechanics but also to quantum field theory. Inequivalent representations of canonical anticommutation relations, states and observables, observable algebras for certain simple cases, the ground state, the equilibrium state at T and O, the Heisenberg model with long-range interaction are covered. (JFP)

Herbert E. Spohn

Rudolf Haag, Nicolaas Marinus Hugenholtz, Marinus Winnink

A. P. Young, Scott Kirkpatrick

The low-temperature behavior of the infinite-range Ising spin-glass model with a Gaussian distribution of interactions is studied by evaluating the statistical mechanics exactly for small systems (up to $N=20$ spins). Our results can be well understood by a simple picture of elementary cluster excitations from the ground state which overturn, on average, of order ${N}^{\frac{1}{2}}$ spins. The conventional definition of the spin-glass order parameter is shown to be unsatisfactory and a new definition is proposed. It is speculated that ensemble averages may give different results from time averages for $N\ensuremath{\rightarrow}\ensuremath{\infty}$ even in the infinite time limit.