Absence of replica symmetry breaking in the Edwards-Anderson model near zero temperature

C. Itoi, H. Shimajiri, Y. Sakamoto

It is proven that the ground state is unique in the Edwards-Anderson model
for almost all continuous random exchange interactions, and any excited state
with the overlap less than its maximal value has large energy in dimensions
higher than two with probability one. Since the spin overlap is shown to be
concentrated at its maximal value in the ground state, replica symmetry
breaking does not occur in the Edwards-Anderson model near zero temperature.