A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance ${r}_{\mathrm{ij}}$ apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance ${r}_{\mathrm{ij}}$ apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.

Physical review. B, Condensed matterJun 10, 20029 citations

Correspondence between long-range and short-range spin glasses

R. A. Baños, L. A. Fernández, Víctor Martín-Mayor +1 more

We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power $\ensuremath{\sigma}$ of the distance. We show that there is a value of $\ensuremath{\sigma}$ of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of $\ensuremath{\sigma}$ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power $\ensuremath{\sigma}$ of the distance. We show that there is a value of $\ensuremath{\sigma}$ of the long-range model for which the critical behavior is very similar to that of the short-range model in four dimensions. We also study a value of $\ensuremath{\sigma}$ for which we find the critical behavior to be compatible with that of the three-dimensional model, although we have much less precision than in the four-dimensional case.

arXiv:1207.7014Physical Review BOct 17, 201250 citations

A study of short-range spin glasses

Haim Sompolinsky, Annette Zippelius

Lecture notes in physicsJan 1, 19830 citations

Entropic long range order in a 3D spin glass model

Maria Chiara Angelini, Federico Ricci‐Tersenghi

We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards–Anderson spin glass model with bimodal couplings ( J = ± 1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and low enough link density), where spins are long range correlated, even if the ground state energy stiffness is null. In other words, in this region twisting the boundary conditions costs no energy, but spins are long range correlated by means of pure entropic effects.We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards–Anderson spin glass model with bimodal couplings ( J = ± 1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and low enough link density), where spins are long range correlated, even if the ground state energy stiffness is null. In other words, in this region twisting the boundary conditions costs no energy, but spins are long range correlated by means of pure entropic effects.

arXiv:1007.1922Journal of Statistical Mechanics Theory and ExperimentFeb 1, 20112 citations

Quantum spin glasses

Subir Sachdev A

Cambridge University Press eBooksApr 7, 20110 citations

A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance

{r}_{\mathrm{ij}}

apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.