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arXiv:cond-mat/0310381

Quantum Spin Glass Phase Boundary in (+/-)J Transverse Field Ising Systems

Arnab Das, Amit Dutta, Bikas K. Chakrabarti

Published Oct 16, 2003• 0 citations
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Abstract

Here we study zero temperature quantum phase transition driven by the transverse field for random $\pm J$ Ising model on chain and square lattice. We present some analytical results for one dimension and some numerical results for very small square lattice under periodic boundary condition. The numerical results are obtained employing exact diagonalization technique following Lanczos method.

DOI
10.48550/arxiv.cond-mat/0310381

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We report exact numerical diagonalization results of the infinite-range Ising spin glass in a transverse field ΓΓΓ at zero temperature. Eigenvalues and eigenvectors are determined for various strengths of ΓΓΓ and for system sizes N≤16N \le 16N≤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 ΓΓΓ. The disorder averaging is done typically over 1000 configurations. Our finite size scaling analysis indicates a spin glass transition at Γc≃1.5Γ_c \simeq 1.5Γc​≃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±0.1z=2.1 \pm 0.1z=2.1±0.1 which is in contradiction with a recent estimate (z=4z=4z=4). Our cumulant analysis indicates the existence of a replica symmetric spin glass phase for Γ<ΓcΓ< Γ_cΓ<Γc​.
We present results of a Monte Carlo simulation study of the zero-temperature quantum phase transition of a three-dimensional short-range spin-1/2 Ising spin glass, driven by a transverse magnetic field. This quantum transition is equivalent to the finite-temperature transition in the (3+1)-dimensional anisotropic classical random Ising model that is the path integral of the quantum system. The critical exponents are estimated using a finite-size scaling analysis. The uniform linear susceptibility is finite at the transition, while the nonlinear susceptibility diverges. The results are more consistent with conventional, rather than activated, dynamic scaling in the quantum system.
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The classical transverse field Ising spin-glass model with short-range interactions is investigated beyond the mean-field approximation for a real d -dimensional lattice. We use an appropriate non-trivial modification of the Bethe-Peierls method recently formulated for the Ising spin-glass. The zero-temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d . The phase diagram is also calculated numerically for different values of d . In the limit , known mean-field results are consistently reproduced.