The Ground State of Continuous Random Exchange Interactions in the Edwards-Anderson Model

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

It is shown that the ground state is unique in the edwards-anderson model for almost all continuous random exchange interactions, and any excited state with the spin overlap less than its maximal value has large energy in dimensions higher than two with probability one.Since the spin overlap is shown to beconcentrated at its maximal value in the ground state, replica symmetrybreaking does not occur in the edwards-anderson model near zero temperature.Pacs numbers : 05.45.+b, 03.65.ud, 11.10.wx it is shown 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 beconcentrated at its maximal value in the ground state, replica symmetrybreaking does not occur in the edwards-anderson model near zero temperature.Pacs numbers : 05.45.+b, 03.65.ud it is shown 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.