arXiv subjects

Hatem Barghathi

Publications and source records attributed to Hatem Barghathi.

25 records · Page 2Linked to original sources

arXiv2015

Strong-randomness phenomena in quantum Ashkin-Teller models

The $N$-color quantum Ashkin-Teller spin chain is a prototypical model for the study of strong-randomness phenomena at first-order and continuous quantum phase transitions. In this paper, we first review the existing strong-disorder renormalization group approaches to the random quantum Ashkin-Teller chain in the weak-coupling as well as the strong-coupling regimes. We then introduce a novel general variable transformation that unifies the treatment of the strong-coupling regime. This allows us to determine the phase diagram for all color numbers $N$, and the critical behavior for all $N \ne 4$. In the case of two colors, $N=2$, a partially ordered product phase separates the paramagnetic and ferromagnetic phases in the strong-coupling regime. This phase is absent for all $N>2$, i.e., there is a direct phase boundary between the paramagnetic and ferromagnetic phases. In agreement with the quantum version of the Aizenman-Wehr theorem, all phase transitions are continuous, even if their clean counterparts are of first order. We also discuss the various critical and multicritical points. They are all of infinite-randomness type, but depending on the coupling strength, they belong to different universality classes.

cond-mat.str-el↗

arXiv2014

Phase Transitions on Random Lattices: How Random is Topological Disorder?

We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems, yielding a wandering exponent of $ω=(d-1)/(2d)$ in $d$ dimensions. %instead of the generic value $ω=1/2$. The stability of clean critical points is thus governed by the criterion $(d+1)ν> 2$ rather than the usual Harris criterion $dν>2$, making topological disorder less relevant than generic randomness. The Imry-Ma criterion is also modified, allowing first-order transitions to survive in all dimensions $d>1$. These results explain a host of puzzling violations of the original criteria for equilibrium and nonequilibrium phase transitions on random lattices. We discuss applications, and we illustrate our theory by computer simulations of random Voronoi and other lattices.

cond-mat.dis-nn↗

arXiv2014

Enhanced rare region effects in the contact process with long-range correlated disorder

We investigate the nonequilibrium phase transition in the disordered contact process in the presence of long-range spatial disorder correlations. These correlations greatly increase the probability for finding rare regions that are locally in the active phase while the bulk system is still in the inactive phase. Specifically, if the correlations decay as a power of the distance, the rare region probability is a stretched exponential of the rare region size rather than a simple exponential as is the case for uncorrelated disorder. As a result, the Griffiths singularities are enhanced and take a non-power-law form. The critical point itself is of infinite-randomness type but with critical exponent values that differ from the uncorrelated case. We report large-scale Monte-Carlo simulations that verify and illustrate our theory. We also discuss generalizations to higher dimensions and applications to other systems such as the random transverse-field Ising model, itinerant magnets and the superconductor-metal transition.

cond-mat.stat-mech↗

arXiv2014

Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations

We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.

cond-mat.stat-mech↗

arXiv2012

Random fields at a nonequilibrium phase transition

We investigate nonequilibrium phase transitions in the presence of disorder that locally breaks the symmetry between two equivalent macroscopic states. In low-dimensional equilibrium systems, such "random-field" disorder is known to have dramatic effects: It prevents spontaneous symmetry breaking and completely destroys the phase transition. In contrast, we demonstrate that the phase transition of the one-dimensional generalized contact process persists in the presence of random field disorder. The dynamics in the symmetry-broken phase becomes ultraslow and is described by a Sinai walk of the domain walls between two different absorbing states. We discuss the generality and limitations of our theory, and we illustrate our results by means of large-scale Monte-Carlo simulations.

cond-mat.stat-mech↗

arXiv2011

Infinite-randomness criticality in a randomly layered Heisenberg magnet

We study the ferromagnetic phase transition in a randomly layered Heisenberg magnet using large-scale Monte-Carlo simulations. Our results provide numerical evidence for the infinite-randomness scenario recently predicted within a {strong-disorder renormalization group approach}. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. We also study the perpendicular and parallel spin-wave stiffnesses in the Griffiths phase. In agreement with the theoretical predictions, the parallel stiffness is nonzero for all temperatures $T<T_c$. In contrast, the perpendicular stiffness remains zero in part of the ordered phase, giving rise to anomalous elasticity. In addition, we calculate the in-plane correlation length which diverges already inside the disordered phase at a temperature significantly higher than $T_c$. The time autocorrelation function within model $A$ dynamics displays an ultraslow logarithmic decay at criticality and a nonuniversal power-law in the Griffiths phase.

cond-mat.stat-mech↗

arXiv2010

Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.

cond-mat.str-el↗