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Acta Physica Sinica

THREE-DIMENSIONAL QUANTUM SPIN GLASS THEORY(III) ──REPLICA SYMMETRY BREAKING SOLUTION

Ao K

Published Jan 1, 1996• 0 citations
OpenAlex

Abstract

Using generalized Parisi's replica symmetry breaking scheme, the quantum spin glasstheory proposed by our previous work is extended to the first-step replica symmetry breaking. A set of new self-consistent equations of spin self-interact ions and spin glass order pa rameters are obtained. The corresponding local susceptibility is reduced. It is found that thereplica symmetry solution for vector spin glass model at low temperature must be brokenthrough calculating the free-energy of the replica symmetry breaking.

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Using generalized Parisi's replica symmetry breaking scheme, the quantum spin glasstheory proposed by our previous work is extended to the first-step replica symmetry breaking. A set of new self-consistent equations of spin self-interact ions and spin glass order pa rameters are obtained. The corresponding local susceptibility is reduced. It is found that thereplica symmetry solution for vector spin glass model at low temperature must be brokenthrough calculating the free-energy of the replica symmetry breaking.
Using generalized Parisi's replica symmetry breaking scheme, the quantum spin glass theory proposed by our previous work is extended to the first-step replica symmetry breaking. A set of new self-consistent equations of spin self-interact ions and spin glass order parameters are obtained. The corresponding local susceptibility is reduced. It is found that the replica symmetry solution for vector spin glass model at low temperature must be broken through calculating the free-energy of the replica symmetry breaking.
By employing the imaginary time functional technique and the so-called replica method, a quantum vector spin glass model with random Dzyaloshinskii-Moriya anisotropy and ferro-magnetic interaction is investigated for any spin quantum numbers. In the static replica sym-metry limit, the spin self-interaction order parameters, the spin glass order parameters and the magnetization are all determined self-consistently. The relation between susceptibility tensors and order parameters is set up. Compared with other methods, our theory works at all tempe-ratures.
Parisi's replica-symmetry-breaking scheme is applied to the quantum Sherrington-Kirkpatrick Ising spin glass in a transverse magnetic field. The order-parameter function q(x) is calculated near Tf{\mathit{T}}_{\mathit{f}}Tf​, while for all temperatures the first stage of replica-symmetry breaking is calculated. Internal energy, entropy, and magnetic susceptibility are calculated in order to investigate the quality of both the replica-symmetric and the replica-symmetry-broken theories.
The stability of Parisi's solution (1979-80) of the infinite-range spin glass model is examined near the transition temperature. It is found that the quadratic terms in the variation of the free energy are all non-positive. The free energy is only a local maximum with respect to q(x) if q is constrained to be a monotonic function of x. The connection between replica symmetry breaking and failure of linear response theory for magnetic susceptibility is shown in more detail. It is shown that the order parameter susceptibility is divergent, as expected, in the spin glass phase.
The Ising infinite-range spin-glass model with p-spin interactions in the presence of a transverse field is studied for large but finite p using the Matsubara time representation and Parisi's scheme of replica-symmetry breaking. In the spin-glass phase, the corrections to the limit appear much more essential than in the classical counterpart. It is shown that the quantum fluctuations have the effect of destroying the spin-glass order and a lower temperature is required to stabilize the spin-glass phase. The spin autocorrelation function in the spin-glass phase is explicitly calculated as a function of p and the Matsubara time. The result is just complementary and consistent with that previously obtained for the paramagnetic state without using the replica method.