Transverse ising spin glass model for quantum spin glass system

Abstract

In this paper we investigate for the infinite-range Ising spin glass model (i.e., Sherrington-Kirkpatrick (SK) model) with a transverse field under static approximation by using the imaginary-time replica formalism. From the investigations we show three important results: First, we show that a replica-symmetric quantum spin glass phase is stable in most of the area of spin glass phase in the temperature-transverse field phase diagram. This confirms the existence of stable replica-symmetric spin glass phase under static approximation, which is contrary to some previous results derived without the static approximation where the replica-symmetric solution is always unstable in the whole spin glass phase. Secondly, we show our theoretical result of nonlinear susceptibility $X_nl$ which conforms to the experimental result of nonlinear susceptibility measurement by Wu et al. [Phys. Rev. Lett. 71, 1919 (1993)] in a quantum spin glass $LiHo_xY_{1-x}F_4$. Thirdly, in classical (SK) spin glass system, we confirm the anomaly in the second temperature derivative of $C_H/T$ near the glass transition temperature $T_g$, associated possibly with the field-dependent variation of entropy in the spin glass transition, which agrees with the previous experimental observation in a classical spin glass system CuMn by Fogle et al. [Phys. Rev. Lett. 50, 1815 (1983)]. We also show that this anomaly is suppressed by the nonzero transverse field of quantum spin glass system, by which we can check for the quantum tunneling competing against spin freezing.