Complex replica zeros of ±J Ising spin glass at zero temperature

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.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.

Aug 3, 20137 citations

Zero-temperature transition in a classical transverse Ising spin glass

R. Pirc, Peter Prelovšek, Bosiljka Tadić

Solid State CommunicationsOct 1, 19874 citations

Quantum transverse Ising spin-glass model in the mean-field approximation

Katarzyna Walasek, K. Lukierska‐Walasek

A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$, $T$ plane is also given.A mean-field approximation is used to investigate the quantum transverse Ising spin-glass model in the Edwards-Anderson version. We introduce two order parameters, diagonal and off diagonal in replica indices, and discuss their physical significance. The effective free-energy function is obtained, and the critical value of the transverse field $\ensuremath{\Gamma}$ at zero temperature is calculated. We find the behavior of the order parameters near the zero-temperature critical point. The phase diagram in the $\ensuremath{\Gamma}$,$T$ plane is also given.

Physical review. B, Condensed matterOct 1, 198632 citations

T

plane is also given.