Dissipative quantum disordered models

This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.Comment: Contribution to the 12th International Conference on Recent Progress in Many-Body Theories, Santa Fe, New Mexico, USA, August 2004; 10 pages no fig

Temporally disordered Ising models

We present a study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations. We reproduce some well known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as for example, globally fluctuating temperatures or random fields). All the predictions coming from our field theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed.Comment: Submitted to Phys. Rev. E. Rapid Comm. 4 page

Concentration inequalities for disordered models

We use a generalization of Hoeffding's inequality to show concentration results for the free energy of disordered pinning models, assuming only that the disorder has a finite exponential moment. We also prove some concentration inequalities for directed polymers in random environment, which we use to establish a large deviations results for the end position of the polymer under the polymer measure.Comment: Revised versio

Randomly Broken Nuclei and Disordered Systems

Similarities between models of fragmenting nuclei and disordered systems in condensed matter suggest corresponding methods. Several theoretical models of fragmentation investigated in this fashion show marked differences, indicating possible new methods for distinguishing models using yield data. Applying nuclear methods to disordered systems also yields interesting results.Comment: 10 pages, 4 figure

Correlated disordered interactions on Potts models

Using a weak-disorder scheme and real-space renormalization-group techniques, we obtain analytical results for the critical behavior of various q-state Potts models with correlated disordered exchange interactions along d1 of d spatial dimensions on hierarchical (Migdal-Kadanoff) lattices. Our results indicate qualitative differences between the cases d-d1=1 (for which we find nonphysical random fixed points, suggesting the existence of nonperturbative fixed distributions) and d-d1>1 (for which we do find acceptable perturbartive random fixed points), in agreement with previous numerical calculations by Andelman and Aharony. We also rederive a criterion for relevance of correlated disorder, which generalizes the usual Harris criterion.Comment: 8 pages, 4 figures, to be published in Physical Review

Phase separation in disordered exclusion models

The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically induces phase separation in a range of densities. In the particlewise case the existence of stationary product measures in the homogeneous phase implies that the critical density can be computed exactly, while for sitewise disorder only bounds are available. The coarsening of phase-separated domains starting from a homogeneous initial condition is addressed using scaling arguments and extremal statistics considerations. Some of these results have been obtained previously in the context of directed polymers subject to columnar disorder.Comment: 15 pages, 4 figure

Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder

We consider disordered models of pinning of directed polymers on a defect line, including (1+1)-dimensional interface wetting models, disordered Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional polymers in interaction with columnar defects. We consider also random copolymers at a selective interface. These models are known to have a (de)pinning transition at some critical line in the phase diagram. In this work we prove that, as soon as disorder is present, the transition is at least of second order: the free energy is differentiable at the critical line, and the order parameter (contact fraction) vanishes continuously at the transition. On the other hand, it is known that the corresponding non-disordered models can have a first order (de)pinning transition, with a jump in the order parameter. Our results confirm predictions based on the Harris criterion.Comment: 4 pages, 1 figure. Version 2: references added, minor changes made. To appear on Phys. Rev. Let

Critical behaviour of the Random--Bond Ashkin--Teller Model, a Monte-Carlo study

The critical behaviour of a bond-disordered Ashkin-Teller model on a square lattice is investigated by intensive Monte-Carlo simulations. A duality transformation is used to locate a critical plane of the disordered model. This critical plane corresponds to the line of critical points of the pure model, along which critical exponents vary continuously. Along this line the scaling exponent corresponding to randomness $\phi=(\alpha/\nu)$ varies continuously and is positive so that randomness is relevant and different critical behaviour is expected for the disordered model. We use a cluster algorithm for the Monte Carlo simulations based on the Wolff embedding idea, and perform a finite size scaling study of several critical models, extrapolating between the critical bond-disordered Ising and bond-disordered four state Potts models. The critical behaviour of the disordered model is compared with the critical behaviour of an anisotropic Ashkin-Teller model which is used as a refference pure model. We find no essential change in the order parameters' critical exponents with respect to those of the pure model. The divergence of the specific heat $C$ is changed dramatically. Our results favor a logarithmic type divergence at $T_{c}$, $C\sim \log L$ for the random bond Ashkin-Teller and four state Potts models and $C\sim \log \log L$ for the random bond Ising model.Comment: RevTex, 14 figures in tar compressed form included, Submitted to Phys. Rev.