Impurity disorder vs random magnetic field disorder: consequences of long-range correlations in a quantum critical point

Mau-chung Chang, Elihu Abrahams

The effect of the long-range correlated random magnetic fields which behave like $〈h(x)h(y)〉$ $\ensuremath{\sim}\frac{1}{{|x\ensuremath{-}y|}^{d\ensuremath{-}\ensuremath{\sigma}}}$ on the critical phenomena is discussed with the use of the nonlinear $\ensuremath{\sigma}$ model. The crossover between the two critical behaviors dominated by the long-range and short-range disorder fixed points is shown to occur at $(m\ensuremath{-}2)\ensuremath{\sigma}\ensuremath{-}d+4=0$ ($m$ is the spin dimensionality). The critical exponents calculated at the long-range disorder fixed point around the lower critical dimensionality $4+\ensuremath{\sigma}$ are not the same as those in $d\ensuremath{-}2$ expansions in the pure system.

Dimo I. Uzunov, E. R. Kokutcheva, YONKO T. MILLEV

Heiko Rieger, Ferenc Iglói

We study the effect of spatial correlations on quenched disorder in random quantum magnets at and near a quantum critical point. In random transverse-field Ising systems disorder correlations that decay algebraically with an exponent $\ensuremath{\rho}$ change the universality class of the transition for small enough $\ensuremath{\rho}$, and off-critical Griffiths-McCoy singularities are enhanced. We present exact results for 1D utilizing a mapping to fractional Brownian motion and generalize the predictions for the critical exponents and the generalized dynamical exponent in the Griffiths phase to $d\ensuremath{\ge}2$.

I. P. Takov

Björn Ahrens, Alexander K. Hartmann

We study the correlated-disorder-driven zero-temperature equilibrium phase transition of the random-field Ising magnet (RFIM) using exact numerical ground-state calculations for cubic lattices. We consider correlations of the quenched disorder decaying proportionally to ${r}^{a}$, where $r$ is the distance between two lattice sites and $a<0$. To obtain exact ground states, we use a well-established mapping to the graph-theoretical maximum-flow problem, which allows us to study large system sizes of more than $2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ spins. We use finite-size-scaling analyses for values $a={\ensuremath{-}1,\ensuremath{-}2,\ensuremath{-}3,\ensuremath{-}7}$ to calculate the critical point and the critical exponents characterizing the behavior of the specific heat, magnetization, susceptibility, and the correlation length close to the critical point. We find basically the same critical behavior as for the RFIM with $\ensuremath{\delta}$-correlated disorder, except for the finite-size exponent of the susceptibility and for the case $a\ensuremath{\ge}\ensuremath{-}2$, where the results are also compatible with a phase transition at infinitesimal disorder strength. We numerically confirm earlier predictions.

Hennadii Yerzhakov, Joseph Maciejko