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.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.

arXiv:cond-mat/9412032Physical review. B, Condensed matterJul 1, 1995165 citations

Mean field and ε -expansion study of spin glasses

Jing-Huei Chen, T. C. Lubensky

A Landau-Ginzburg phenomenological free energy for the Edwards and Anderson spin-glass model when there is competition between spin-glass and ferromagnetic ordering is developed. This free energy obtained with the use of the $n\ensuremath{\rightarrow}0$ replication procedure is analyzed using mean-field theory and the $\ensuremath{\epsilon}$ expansion. Critical exponents for the ferromagnetic-spin-glass multicritical point are calculated in $6\ensuremath{-}\ensuremath{\epsilon}$ dimensions. For Ising systems, $\ensuremath{\nu}=\frac{1}{2}+(\frac{2}{3})\ensuremath{\epsilon}$ and $\ensuremath{\varphi}=1+(\frac{1}{2})\ensuremath{\epsilon}$. For $\mathrm{XY}$ and Heisenberg systems, these exponents are complex. This result is not fully understood. The Harris-Plischke-Zuckermann model for amorphous magnetism is shown to have an Ising-like spin-glass fixed point in high enough dimension.A Landau-Ginzburg phenomenological free energy for the Edwards and Anderson spin-glass model when there is competition between spin-glass and ferromagnetic ordering is developed. This free energy obtained with the use of the $n\ensuremath{\rightarrow}0$ replication procedure is analyzed using mean-field theory and the $\ensuremath{\epsilon}$ expansion. Critical exponents for the ferromagnetic-spin-glass multicritical point are calculated in $6\ensuremath{-}\ensuremath{\epsilon}$ dimensions. For Ising systems, $\ensuremath{\nu}=\frac{1}{2}+(\frac{2}{3})\ensuremath{\epsilon}$ and $\ensuremath{\varphi}=1+(\frac{1}{2})\ensuremath{\epsilon}$. For $\mathrm{XY}$ and Heisenberg systems, these exponents are complex. This result is not fully understood. The Harris-Plischke-Zuckermann model for amorphous magnetism is shown to have an Ising-like spin-glass fixed point in high enough dimension.

Physical review. B, Solid stateSep 1, 1977155 citations

Quantum Spin Glasses at Strong Disorder

Ferenc Pázmándi

APSMar 1, 19970 citations

Scaling properties of quantum spin glasses

Mai Suan Li, Marek Cieplak

Physica A Statistical Mechanics and its ApplicationsJun 1, 19941 citation

Solvable spin glass of quantum rotors

J. Ye, Subir Sachdev A, N. Read

We examine a model of M-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. A complete solution is obtained at M=\ensuremath{\infty} in the spin-glass and quantum-disordered phases. The quantum phase transition separating them is found to possess logarithmic violations of scaling, with no further modifications to the leading critical behavior at any order in 1/M; this suggests that the critical properties of the transverse-field Ising model (believed to be identical to the M\ensuremath{\rightarrow}1 limit) are the same as those of the M=\ensuremath{\infty} quantum rotors.We examine a model of M-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. A complete solution is obtained at M=\ensuremath{\infty} in the spin-glass and quantum-disordered phases. The quantum phase transition separating them is found to possess logarithmic violations of scaling, with no further modifications to the leading critical behavior at any order in 1/M; this suggests that the critical properties of the transverse-field Ising model (believed to be identical to the M\ensuremath{\rightarrow}1 limit) are the same as those of the M=\ensuremath{\infty} quantum rotors.

arXiv:cond-mat/9212027Physical Review LettersJun 21, 1993145 citations

\mathrm{XY}

and Heisenberg systems, these exponents are complex. This result is not fully understood. The Harris-Plischke-Zuckermann model for amorphous magnetism is shown to have an Ising-like spin-glass fixed point in high enough dimension.