# Accession Number:

## AD0429544

# Title:

## A PROOF THAT THE FREE ENERGY OF A SPIN SYSTEM IS EXTENSIVE,

# Descriptive Note:

# Corporate Author:

## CALIFORNIA UNIV SAN DIEGO LA JOLLA

# Personal Author(s):

# Report Date:

## 1964-01-01

# Pagination or Media Count:

## 29.0

# Abstract:

The fre energy obtained from the canonical partition function for a finite spin system possesses a certain convexity property, of which theorems by Peierls and Bogoliubov are particular applications. This property is used in proving the following result the free energy of a spin sys tem in a regular lattice, divided by the number of spins, converges to a definite limit as the system becomes infinite in such a way that the surface to volume ratio goes to zero. The limit is not influenced by certain common types of boundary conditions. A similar result, but with convergence understood in a weaker sense, holds for derivatives of the free energy such as entropy, magnetization, and specific heat. In the proof it is necessary to assume that the Hamiltonian has the translational symmetry of the spin system, and that long range interactions decrease sufficiently rapidly with the distance r between spins. Author