Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the universality class of the 3d Ising model with long-range-correlated disorder
111
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We analyze a controversial question about the universality class of the three-dimensional Ising model with long-range-correlated disorder. Whereas both analytical and numerical studies performed so far support an extended Harris criterion (A. Weinrib, B. I. Halperin, Phys. Rev. B 27 (1983) 413) and bring about the new universality class, the numerical values of the critical exponents found so far differ essentially. To resolve this discrepancy we perform extensive Monte Carlo simulations of a 3d Ising magnet with non-magnetic impurities arranged as lines with random orientation. We apply Wolff cluster algorithm accompanied by a histogram reweighting technique and make use of the finite-size scaling to extract the values of critical exponents governing the magnetic phase transition. Our estimates for the exponents differ from the results of the two numerical simulations performed so far and are in favour of a non-trivial dependency of the critical exponents on the peculiarities of long-range correlations decay.
rate research
Read More
We study critical behavior of the diluted 2D Ising model in the presence of disorder correlations which decay algebraically with distance as $sim r^{-a}$. Mapping the problem onto 2D Dirac fermions with correlated disorder we calculate the critical properties using renormalization group up to two-loop order. We show that beside the Gaussian fixed point the flow equations have a non trivial fixed point which is stable for $0.995<a<2$ and is characterized by the correlation length exponent $ u= 2/a + O((2-a)^3)$. Using bosonization, we also calculate the averaged square of the spin-spin correlation function and find the corresponding critical exponent $eta_2=1/2-(2-a)/4+O((2-a)^2)$.
We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reasonably well established, the predicted exponents are controversial. We propose a method of growing such correlated disorder using the three-dimensional Ising model as benchmark systems both for generating disorder and studying the resulting phase transition. Critical equilibrium configurations of a disorder-free system are used to define the two-value distributed random bonds with a small power-law exponent given by the pure Ising exponent. Finite-size scaling analysis shows a new universality class with a single phase transition, but the critical exponents $ u_d=1.13(5), eta_d=0.48(3)$ differ significantly from theoretical predictions. We find that depending on details of the disorder generation, disorder-averaged quantities can develop peaks at two temperatures for finite sizes. Finally, a layer model with the two values of bonds spatially separated to halves of the system genuinely has multiple phase transitions and thermodynamic properties can be flexibly tuned by adjusting the model parameters.
The standard two-dimensional Ising spin glass does not exhibit an ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as $(1+r^2)^{-a/2}$, $a>0$. We study numerically with exact algorithms the ground state and domain wall excitations. Our results indicate that the inclusion of bond correlations does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro/antiferromagnetic domains into the system. The length scale of ferro/antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, $a to a_c = 0$. Thus, our results suggest that the system becomes a ferro/antiferromagnet only in the limit $a to 0$.
We show that spatial resolved dissipation can act on Ising lattices molding the universality class of their critical points. We consider non-local spin losses with a Liouvillian gap closing at small momenta as $propto q^alpha$, with $alpha$ a positive tunable exponent, directly related to the power-law decay of the spatial profile of losses at long distances. The associated quantum noise spectrum is gapless in the infrared and it yields a class of soft modes asymptotically decoupled from dissipation at small momenta. These modes are responsible for the emergence of a critical scaling regime which can be regarded as the non-unitary analogue of the universality class of long-range interacting Ising models. In particular, for $0<alpha<1$ we find a non-equilibrium critical point ruled by a dynamical field theory ascribable to a Langevin model with coexisting inertial ($proptoomega^2$) and frictional ($proptoomega$) kinetic coefficients, and driven by a gapless Markovian noise with variance $propto q^alpha$ at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Furthermore, by employing a one-loop improved RG calculation, we estimate the conditions for observability of this scaling regime before incoherent local emission intrudes in the spin sample, dragging the system into a thermal fixed point. We also explore other instances of criticality which emerge for $alpha>1$ or adding long-range spin interactions. Our work lays out perspectives for a revision of universality in driven-open systems by employing dark states supported by non-local dissipation.
We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum $S(k) sim 1/k^{alpha}$ with $alpha > 0$. Moura and Lyra [Phys. Rev. Lett. {bf 81}, 3735 (1998)] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided $alpha > 2$. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
