6 research outputs found
Zero Temperature Dynamics of 2D and 3D Ising Ferromagnets
We consider zero-temperature, stochastic Ising models with nearest-neighbor
interactions in two and three dimensions. Using both symmetric and asymmetric
initial configurations, we study the evolution of the system with time. We
examine the issue of convergence of the dynamics and discuss the nature of the
final state of the system. By determining a relation between the median number
of spin flips per site, the probability p that a spin in the initial spin
configuration takes the value +1, and lattice size, we conclude that in two and
three dimensions, the system converges to a frozen (but not necessarily
uniform) state when p is not equal to 1/2. Results for p=1/2 in three
dimensions are consistent with the conjecture that the system does not evolve
towards a fully frozen limiting state. Our simulations also uncover `striped'
and `blinker' states first discussed by Spirin et al., and their statistical
properties are investigated.Comment: 17 pages, 12 figure
Against Chaos in Temperature in Mean-Field Spin-Glass Models
We study the problem of chaos in temperature in some mean-field spin-glass
models by means of a replica computation over a model of coupled systems. We
propose a set of solutions of the saddle point equations which are
intrinsically non-chaotic and solve a general problem regarding the consistency
of their structure. These solutions are relevant in the case of uncoupled
systems too, therefore they imply a non-trivial overlap distribution
between systems at different temperatures. The existence of such
solutions is checked to fifth order in an expansion near the critical
temperature through highly non-trivial cancellations, while it is proved that a
dangerous set of such cancellations holds exactly at all orders in the
Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is
also considered obtaining analogous results. Previous analytical results are
discussed.Comment: 20 pages, submitted to J.Phys.
Disordered ultracold atomic gases in optical lattices: A case study of Fermi-Bose mixtures
We present a review of properties of ultracold atomic Fermi-Bose mixtures in
inhomogeneous and random optical lattices. In the strong interacting limit and
at very low temperatures, fermions form, together with bosons or bosonic holes,
{\it composite fermions}. Composite fermions behave as a spinless interacting
Fermi gas, and in the presence of local disorder they interact via random
couplings and feel effective random local potential. This opens a wide variety
of possibilities of realizing various kinds of ultracold quantum disordered
systems. In this paper we review these possibilities, discuss the accessible
quantum disordered phases, and methods for their detection. The discussed
quantum phases include Fermi glasses, quantum spin glasses, "dirty"
superfluids, disordered metallic phases, and phases involving quantum
percolation.Comment: 29 pages and 11 figure
The Potts Fully Frustrated model: Thermodynamics, percolation and dynamics in 2 dimensions
We consider a Potts model diluted by fully frustrated Ising spins. The model
corresponds to a fully frustrated Potts model with variables having an integer
absolute value and a sign. This model presents precursor phenomena of a glass
transition in the high-temperature region. We show that the onset of these
phenomena can be related to a thermodynamic transition. Furthermore this
transition can be mapped onto a percolation transition. We numerically study
the phase diagram in 2 dimensions (2D) for this model with frustration and {\em
without} disorder and we compare it to the phase diagram of the model with
frustration {\em and} disorder and of the ferromagnetic model.
Introducing a parameter that connects the three models, we generalize the exact
expression of the ferromagnetic Potts transition temperature in 2D to the other
cases. Finally, we estimate the dynamic critical exponents related to the Potts
order parameter and to the energy.Comment: 10 pages, 10 figures, new result
The metastate approach to thermodynamic chaos
In realistic disordered systems, such as the Edwards-Anderson (EA) spin
glass, no order parameter, such as the Parisi overlap distribution, can be both
translation-invariant and non-self-averaging. The standard mean-field picture
of the EA spin glass phase can therefore not be valid in any dimension and at
any temperature. Further analysis shows that, in general, when systems have
many competing (pure) thermodynamic states, a single state which is a mixture
of many of them (as in the standard mean-field picture) contains insufficient
information to reveal the full thermodynamic structure. We propose a different
approach, in which an appropriate thermodynamic description of such a system is
instead based on a metastate, which is an ensemble of (possibly mixed)
thermodynamic states. This approach, modelled on chaotic dynamical systems, is
needed when chaotic size dependence (of finite volume correlations) is present.
Here replicas arise in a natural way, when a metastate is specified by its
(meta)correlations. The metastate approach explains, connects, and unifies such
concepts as replica symmetry breaking, chaotic size dependence and replica
non-independence. Furthermore, it replaces the older idea of non-self-averaging
as dependence on the bulk couplings with the concept of dependence on the state
within the metastate at fixed coupling realization. We use these ideas to
classify possible metastates for the EA model, and discuss two scenarios
introduced by us earlier --- a nonstandard mean-field picture and a picture
intermediate between that and the usual scaling/droplet picture.Comment: LaTeX file, 49 page
Metastable States in Spin Glasses and Disordered Ferromagnets
We study analytically M-spin-flip stable states in disordered short-ranged
Ising models (spin glasses and ferromagnets) in all dimensions and for all M.
Our approach is primarily dynamical and is based on the convergence of a
zero-temperature dynamical process with flips of lattice animals up to size M
and starting from a deep quench, to a metastable limit. The results (rigorous
and nonrigorous, in infinite and finite volumes) concern many aspects of
metastable states: their numbers, basins of attraction, energy densities,
overlaps, remanent magnetizations and relations to thermodynamic states. For
example, we show that their overlap distribution is a delta-function at zero.
We also define a dynamics for M=infinity, which provides a potential tool for
investigating ground state structure.Comment: 34 pages (LaTeX); to appear in Physical Review