Spin Glass Transition in Systems with Short-Range Exchange and Random Long-Range Couplings.

We consider the spin-glass (SG) with long-range (LR) random exchange interaction varying with distance $R$ as ${R}^{\ensuremath{-}\frac{d}{2}\ensuremath{-}\frac{\ensuremath{\sigma}}{2}}$, where $d$ is the space dimensionality and $\ensuremath{\sigma}>0$. It is shown that the LR fixed point is stable if $\ensuremath{\sigma}<2$. The nonclassical ($d<3\ensuremath{\sigma}$) LR critical exponents in powers of $3\ensuremath{\sigma}\ensuremath{-}d$ are not continuous at $\ensuremath{\sigma}=2$ when the transition to short-range (SR) exchange is made.We consider the spin-glass (SG) with long-range (LR) random exchange interaction varying with distance $R$ as ${R}^{\ensuremath{-}\frac{d}{2}\ensuremath{-}\frac{\ensuremath{\sigma}}{2}}$, where $d$ is the space dimensionality and $\ensuremath{\sigma}>0$. It is shown that the LR fixed point is stable if $\ensuremath{\sigma}<2$. The nonclassical ($d<3\ensuremath{\sigma}$) LR critical exponents in powers of $3\ensuremath{\sigma}\ensuremath{-}d$ are not continuous at $\ensuremath{\sigma}=2$ when the transition to short-range (SR) exchange is made.

Physical review. B, Condensed matterMar 1, 198418 citations

Critical behavior in random-spin systems with long-range interactions

Yoshitake Yamazaki

Physica A Statistical Mechanics and its ApplicationsMar 1, 19787 citations

Quantum spin glass with long-range random interactions

Amit Dutta

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

Spin-glass properties of ± J random-bond model

Hiroshi Betsuyaku

Journal of Magnetism and Magnetic MaterialsFeb 1, 19832 citations

Field Theory for Site-Disordered Spin Glasses

Theo M. Nieuwenhuizen

In realistic spin glasses a fraction c of spins is located at random positions. Their couplings are determined by the relative spin positions. For such systems a field theory is formulated. In a certain mean-field limit it generalizes the Sherrington-Kirkpatrick free energy of a random bond spin glass. In general, an infinity of multistate overlaps occurs, as in the diluted random bond spin glass of Viana and Bray. For small c there occurs a percolation transition for short-range exchange and the "concentration scaling" T G ∼ c for RKKY couplings.In realistic spin glasses a fraction c of spins is located at random positions. Their couplings are determined by the relative spin positions. For such systems a field theory is formulated. In a certain mean-field limit it generalizes the Sherrington-Kirkpatrick free energy of a random bond spin glass. In general, an infinity of multistate overlaps occurs, as in the diluted random bond spin glass of Viana and Bray. For small c there occurs a percolation transition for short-range exchange and the "concentration scaling" T G ∼ c for RKKY couplings.

Europhysics Letters (EPL)Dec 20, 199310 citations

We consider the spin-glass (SG) with long-range (LR) random exchange interaction varying with distance

R

as ${R}^{\ensuremath{-}\frac{d}{2}\ensuremath{-}\frac{\ensuremath{\sigma}}{2}}$, where

d

is the space dimensionality and $\ensuremath{\sigma}>0$. It is shown that the LR fixed point is stable if $\ensuremath{\sigma}<2$. The nonclassical ($d<3\ensuremath{\sigma}$) LR critical exponents in powers of $3\ensuremath{\sigma}\ensuremath{-}d$ are not continuous at $\ensuremath{\sigma}=2$ when the transition to short-range (SR) exchange is made.

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.