9 research outputs found
Nematic phase in the J1-J2 square-lattice Ising model in an external field
© 2015 American Physical Society. The J1-J2 Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ=J2/|J1| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.Peer Reviewe
Microscopic dynamics underlying the anomalous diffusion
The time dependent Tsallis statistical distribution describing anomalous
diffusion is usually obtained in the literature as the solution of a non-linear
Fokker-Planck (FP) equation [A.R. Plastino and A. Plastino, Physica A, 222, 347
(1995)]. The scope of the present paper is twofold. Firstly we show that this
distribution can be obtained also as solution of the non-linear porous media
equation. Secondly we prove that the time dependent Tsallis distribution can be
obtained also as solution of a linear FP equation [G. Kaniadakis and P.
Quarati, Physica A, 237, 229 (1997)] with coefficients depending on the
velocity, that describes a generalized Brownian motion. This linear FP equation
is shown to arise from a microscopic dynamics governed by a standard Langevin
equation in presence of multiplicative noise.Comment: 4 pag. - no figures. To appear on Phys. Rev. E 62, September 200
Inherent structures dynamics in glasses: a comparative study
A comparative study of the dynamics of inherent structures at low
temperatures is performed on different models of glass formers: a three
dimensional Lennard-Jones binary mixture (LJBM), facilitated spin models
(either symmetrically constrained, SCIC, or asymmetrically, ACIC) and the trap
model. We use suitable correlation functions introduced in a previous work
which allow to distinguish the behaviour between models with or without spatial
or topological structure. Furthermore, the correlations between inherent
structures behave differently in the cases of strong (SCIC) and fragile (ACIC,
LJBM) glasses, as a consequence of the different role played by energy barriers
when the temperature is lowered. The similarities in the behaviour of the ACIC
and LJBM suggest a common nature of the glassy dynamics for both systems.Comment: Proceedings of NEXT2003 (News and Expectations in Thermostatistics,
Sardinia, Italy, september 2003
Anomalous diffusion and Tsallis statistics in an optical lattice
We point out a connection between anomalous quantum transport in an optical
lattice and Tsallis' generalized thermostatistics. Specifically, we show that
the momentum equation for the semiclassical Wigner function that describes
atomic motion in the optical potential, belongs to a class of transport
equations recently studied by Borland [PLA 245, 67 (1998)]. The important
property of these ordinary linear Fokker--Planck equations is that their
stationary solutions are exactly given by Tsallis distributions. Dissipative
optical lattices are therefore new systems in which Tsallis statistics can be
experimentally studied.Comment: 4 pages, 1 figur
Scaling properties in off equilibrium dynamical processes
In the present paper, we analyze the consequences of scaling hypotheses on
dynamic functions, as two times correlations . We show, under general
conditions, that must obey the following scaling behavior , where the scaling variable is
and , two
undetermined functions. The presence of a non constant exponent
signals the appearance of multiscaling properties in the dynamics.Comment: 6 pages, no figure
Dynamics of the frustrated Ising lattice gas
The dynamical properties of a three dimensional model glass, the frustrated
Ising lattice gas (FILG) are studied by Monte Carlo simulations. We present
results of compression experiments, where the chemical potential is either
slowly or abruptly changed, as well as simulations at constant density. One
time quantities like density and two time ones like correlations, responses and
mean square displacements are measured, and the departure from equilibrium
clearly characterized. The aging scenario, particularly in the case of density
autocorrelations is reminiscent of spin glass phenomenology with violations of
the Fluctuation-dissipation theorem, typical of systems with one replica
symmetry breaking. The FILG, as a valid on-lattice model of structural glasses
can be described with tools developed in spin glass theory and, being a finite
dimensional model, can open the way for a systematic study of activated
processes in glasses.Comment: to appear in Phys. Rev. E, november (2000
Thermodynamic Description of the Relaxation of Two-Dimensional Euler Turbulence Using Tsallis Statistics
Euler turbulence has been experimentally observed to relax to a
metaequilibrium state that does not maximize the Boltzmann entropy, but rather
seems to minimize enstrophy. We show that a recent generalization of
thermodynamics and statistics due to Tsallis is capable of explaining this
phenomenon in a natural way. The maximization of the generalized entropy
for this system leads to precisely the same profiles predicted by the
Restricted Minimum Enstrophy theory of Huang and Driscoll. This makes possible
the construction of a comprehensive thermodynamic description of Euler
turbulence.Comment: 15 pages, RevTe
Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
We investigate the relation between two-time, multi-spin, correlation and
response functions in the non-equilibrium critical dynamics of Ising models in
d=1 and d=2 spatial dimensions. In these non-equilibrium situations, the
fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT
`violations' qualitatively similar to those reported in various glassy
materials, but quantitatively dependent on the chosen observable, in contrast
to the results obtained in infinite-range glass models. Nevertheless, all FDT
violations can be understood by considering separately the contributions from
large wavevectors, which are at quasi-equilibrium and obey FDT, and from small
wavevectors where a generalized FDT holds with a non-trivial limit
fluctuation-dissipation ratio X. In d=1, we get X = 1/2 for spin observables,
which measure the orientation of domains, while X = 0 for observables that are
sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a
unique X = 0.34 for all observables. Measurement protocols for X are discussed
in detail. Our results suggest that the definition of an effective temperature
Teff = T / X for large length scales is generically possible in non-equilibrium
critical dynamics.Comment: 26 pages, 10 figure