Spontaneous symmetry breaking in spin glasses

Abstract

The authors discuss the effect of a small uniform symmetry breaking field on the Sherrington-Kirkpatrick (1978) spin glass model. Both q(h)=((S_i)_T²)_J and q_ij(h)=N((S_i)_T(S_j)_T-(S_iS_j)_T)_J are given by scaling functions, f(h/h^*) and g(h/h^*) respectively, where h^*=T/N¹2/. They show that g(x)=xf'(x) so that in the symmetry broken situation (h/h^* to infinity but h<ij=0. The latter is in contrast to the conclusions of Young and Kirkpatrick based on numerical evidence for small samples. They discuss the reasons for this discrepancy.