Theory of an induced-moment spin glass

Hans-Juergen Sommers

Hidetsugu Kitatani, A. Sinada

A new method to calculate the n−th moment of the spin overlap of the two-dimensional ±J Ising model is presented, where the n−th moment of the spin overlap can be calculated as a simple average of the n−th moment of the total spins with a modified bond probability distribution. By this method, the values of the Binder parameter etc. have been calculated extensively with the linear size, L, up to L = 23. The accuracy of the present calculations is similar to that calculated by the conventional transfer matrix method averaging over about 10 5 bond samples. Our results show that the estimation of Tc is strongly affected by the corrections to scaling. Thus, there still remains the possibility of Tc = 0, contrary to the recent results which insist the existence of a finite temperature spin-glass phase transition. 75.50.Lk,02.70.Lq,64.60.Cn,05.50.+q Typeset using REVTEX 1 In the last two decades, investigations of spin-glass problems have been performed

N. Bontemps

Tomoyuki Obuchi, Yoshiyuki Kabashima

Abstract. Zeros of the nth moment of the partition function [Z n] are investigated in a vanishing temperature limit β → ∞, n → 0 keeping y = βn ∼ O(1). In this limit, the moment parameterized by y characterizes the distribution of the ground-state energy. We numerically investigate the zeros for ±J Ising spin glass models with several ladder and tree systems, which can be carried out with a feasible computational cost by a symbolic operation based on the Bethe–Peierls method. For several tree systems we find that the zeros tend to approach the real axis of y in the thermodynamic limit implying that the moment cannot be described by a single analytic function of y as the system size tends to infinity, which may be associated with breaking of the replica symmetry. However, examination of the analytical properties of the moment function and assessment of the spin-glass susceptibility indicate that the breaking of analyticity is relevant to neither one-step or full replica symmetry breaking. § obuchi@stat.phys.titech.ac.jpComplex Replica Zeros of ±J Ising Spin Glass at Zero Temperature 2 1.

Hidetsugu Kitatani, Akira Sinada

A new method to numerically calculate the n th moment of the spin overlap of the two-dimensional ± J Ising model is developed using the identity derived by one of the authors (HK) several years ago. By using the method, the n th moment of the spin overlap can be calculated as a simple average of the n th moment of the total spins with a modified bond probability distribution. The values of the Binder parameter etc have been extensively calculated with the linear size, L , up to L = 23. The accuracy of the calculations in the present method is similar to that in the conventional transfer matrix method with about 10 5 bond samples. The simple scaling plots of the Binder parameter and the spin-glass susceptibility indicate the existence of a finite-temperature spin-glass phase transition. We find, however, that the estimation of T c is strongly affected by the corrections to scaling within the present data ( L ⩽ 23). Thus, there still remains the possibility that T c = 0, contrary to the recent results which suggest the existence of a finite-temperature spin-glass phase transition.

L. Bernardi, Ney Lemke, Pierre‐Olivier Mari +3 more