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Physical review. B, Condensed matter

Quantum spherical description of an Ising spin glass in a transverse field

T. K. Kopec-acute, R. Pirc

Published Mar 1, 1997• 15 citations
Publisher

Abstract

We study the competition between bond randomness and quantum fluctuation in the infinite-range Ising model in the transverse field \ensuremath{\Delta} relevant for a number of pseudospin and magnetic quantum spin-glass systems. By introducing a mapping of the quantum Hamiltonian of the model onto a soft-spin action we consider it truncated version in a form of the solvable quantized spherical model. The resulting critical phase boundary ${\mathrm{T}}_{\mathrm{crit}}$(\ensuremath{\Delta}) is in considerable agreement with the numerical estimates based on the Trotter-Suzuki and Monte Carlo methods. The equation of state for the system is also given.

DOI
10.1103/physrevb.55.5623

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We study the competition between bond randomness and quantum fluctuation in the infinite-range Ising model in the transverse field \ensuremath{\Delta} relevant for a number of pseudospin and magnetic quantum spin-glass systems. By introducing a mapping of the quantum Hamiltonian of the model onto a soft-spin action we consider it truncated version in a form of the solvable quantized spherical model. The resulting critical phase boundary Tcrit{\mathrm{T}}_{\mathrm{crit}}Tcrit​(\ensuremath{\Delta}) is in considerable agreement with the numerical estimates based on the Trotter-Suzuki and Monte Carlo methods. The equation of state for the system is also given.
Abstract We consider the short‐range interaction disordered quantum Ising model with symmetric binary ±J bond distribution on the Bethe lattice (with coordination number z). The system exhibits quantum phase transition separating the spin glass and disordered phases where the quantum effect are regulated by a param‐ eter Δ describing the transverse field. By introducing a mapping of the quantum Hamiltonian of the model onto a soft‐spin action we consider it truncated version in a form of the solvable quantized spherical model. Quantum dynamics is examined via various correlation functions on the infinite tree which are evaluated in a closed form. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The infinite-range Ising spin glass in the presence of a transverse field is considered. Using the generalised Trotter formula and replica methods, the free energy for the system with quenched random bond interactions is evaluated using the static approximation. It is shown that, when the strength of the transverse field equals the largest eigenvalue of the random bond interaction matrix, the spin glass transition is destroyed. The authors also show that a replica-symmetric spin glass phase is stable in a certain region of the temperature-field phase diagram. Finally they present suggestive arguments which indicate that, when the time dependence of the dynamic susceptibility is included, then the stability of the replica-symmetric phase is enhanced.
The infinite-range Ising spin-glass in the presence of a transverse field is studied by Monte Carlo simulations. The overlap probability distribution P ( q ) is defined and calculated for the present quantum case. The P ( q ) in the spin-glass phase has a long tail extended down to q = 0 qualitatively similar to the classical Sherrington-Kirkpatrick model. The phase boundary of the glass transition temperature vs. the transverse field is obtained. Our results for the phase diagram agree with our recent replica symmetry-breaking solution but disagree with the results of Yokata and of Ray et al.
We study the zero-temperature behaviour of the infinite-ranged Ising spin glass in a transverse field. Using spin summation and Monte Carlo methods we characterize the zero-temperature quantum transition. Our results are well compatible with a value for the correlation length exponent, z=4 for the dynamical exponent and an algebraic decay for the imaginary-time correlation function. The zero-temperature Monte Carlo relaxation of the energy in the presence of the transverse field shows that the system monotonically reaches the ground-state energy due to quantum fluctuations and displays glassy effects due to the strong anisotropy in the effective Hamiltonian.
We use quantum Monte Carlo methods and various analytic approximations to study the infinite-range Ising spin-glass model in a transverse field in the disordered phase. We focus on the behavior of the frequency dependent susceptibility of the system above and below the critical field. We establish that, at the quantum critical point, there exists an equivalence between the long-time behavior of this model and that of the single-impurity Kondo model. Our predictions for the long-time dynamics of the model are in good agreement with experimental results on LiHo0.167Y0.833F4{\mathrm{LiHo}}_{0.167}{\mathrm{Y}}_{0.833}{\mathrm{F}}_{4}LiHo0.167​Y0.833​F4​.
We consider quantum rotors or Ising spins in a transverse field on a d-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin-glass and quantum paramagnet phases and a zero-temperature (T) quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions cna be reproduced by minimization of a Landau effective-action functional for the model in finite d with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the T=0 critical point is mapped out as a function of T, strength of the quantum coupling, and applied fields. The spin-glass phase has replica symmetry breaking; but, as in the classical Ising spin glass, the order parameter becomes replica symmetric as T\ensuremath{\rightarrow}0. Next we examine the consequences of fluctuations about the mean field for the critical properties. Above d=8, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above d=8, and for all physical couplings below d=8, we find runaway renormalization-group flows to strong coupling. General scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.