1/mexpansion in spin glasses and the de Almeida-Thouless line

Abstract

It is shown by means of a 1/m expansion about the large-m limit of the m-vector spin glass that the value of the intercept of the de Almeida-Thouless line on the zero temperature axis h(AT) is proportional to T(c)(d), the zero-field transition temperature of the large-m model in d dimensions. Since numerical studies indicate that T(c)(d)=0 for d≤6, it follows that there should be no Almeida-Thouless line for d≤6.