The exact phase diagram of the quantumXY spin glass model in a transverse field (original) (raw)
Journal of the Physical Society of Japan, 2007
The phase diagram of the p-spin-interacting spin glass model in a transverse field is investigated in the limit p → ∞ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit p → ∞ by using the large-p expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.
1997
We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field Γ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of Γ and for system sizes N ≤ 16. We obtain the moments of the distribution of the spin-glass order parameter, the spin-glass susceptibility and the mass gap at different values of Γ. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at Γ c ≃ 1.5. Our estimates for the exponents at the transition are in agreement with those known from other approaches. For the dynamic exponent, we get z = 2.1 ± 0.1 which is in contradiction with a recent estimate (z = 4). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for Γ < Γ c .
Quantum phase transition in spin glasses with multi-spin interactions
Physica a, 1998
We examine the phase diagram of the p-interaction spin glass model in a transverse field. We consider a spherical version of the model and compare with results obtained in the Ising case. The analysis of the spherical model, with and without quantization, reveals a phase diagram very similar to that obtained in the Ising case. In particular, using the static approximation, reentrance is observed at low temperatures in both the quantum spherical and Ising models. This is an artifact of the approximation and disappears when the imaginary time dependence of the order parameter is taken into account. The resulting phase diagram is checked by accurate numerical investigation of the phase boundaries.
Continuous phase transition in a spin-glass model without time-reversal symmetry
1999
Nowadays there is large amount of research being done on the problem of the glass transition from the perspective of spin-glass theory 1, 2. This interest originates from old observations by Kirkpatrick, Thirumalai, and Wolynes 3, who found a striking similarity between the dynamical equations of some mean-field spin-glass models and the mode-coupling equations for glasses.
Quantum Monte Carlo study of the infinite-range Ising spin glass in a transverse field
Journal of Physics A: Mathematical and General, 1996
We study the zero-temperature behavior of the infinite-ranged Ising spin glass in a transverse field. Using spin summation techniques and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value ν = 1 4 for the correlation length exponent, z = 4 for the dynamical exponent and an algebraic decay t −1 for the imaginary-time correlation function. The zero-temperature relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground state energy due to tunneling processes and displays strong glassy effects.
On a classical spin glass model
Zeitschrift f�r Physik B Condensed Matter, 1983
A simple, exactly soluble, model of a spin-glass with weakly correlated disorder is presented. It includes both randomness and frustration, but its solution can be obtained without replicas. As the temperature T is lowered, the spin-glass phase is reached via an equilibrium phase transition at T--T I. The spin-glass magnetization exhibits a distinct S-shape character, which is indicative of a field-induced transition to a state of higher magnetization above a certain threshold field. For suitable probability distributions of the exchange interactions. (a) A mixed phase is found where spin-glass and ferromagnetism coexist. (b) The zero-field susceptibility has a flat plateau for 0_<T_< T~ and a Curie-Weiss behaviour for T > T I. (c) At low temperatures the magnetic specific heat is linearly dependent on the temperature. The physical origin of the dependence upon the probability distributions is explained, and a careful analysis of the ground state structure is given.
Reentrant phases in the ± J spin glass
Physica A: Statistical Mechanics and its Applications, 1996
We consider an enlarged phase space of the +J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro-to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro-to ferromagnetic interations, q; and (iii) the temperature, T. Within this phase space we observe extended regions of the low-temperature spin-glass phase which is characterised by a unique distribution of the local-order parameter. We observe reentrant phase transitions: for fixed p and q with varying T the distribution of the local order parameter shows paramagnetic, ferromagnetic and then spin-glass phases; for fixed p and T and varying q the distribution shows ferromagnetic to paramagnetic and then spin-glass phases.
Dynamical Response of Quantum Spin-Glass Models at T=0
Physical Review Letters, 2001
We study the behavior of two archetypal quantum spin glasses at T 0 by exact diagonalization techniques: the random Ising model in a transverse field and the random Heisenberg model. The behavior of the dynamical spin response is obtained in the spin-glass ordered phase. In both models it is gapless and has the general form x 00 ͑v͒ qd͑v͒ 1 x 00 reg ͑v͒, with x 00 reg ͑v͒ ϳ v for the Ising and x 00 reg ͑v͒ ϳ const for the Heisenberg, at low frequencies. The method provides new insight to the physical nature of the low-lying excitations.