5 research outputs found
Theory of Phase Ordering Kinetics
The theory of phase ordering dynamics -- the growth of order through domain
coarsening when a system is quenched from the homogeneous phase into a
broken-symmetry phase -- is reviewed, with the emphasis on recent developments.
Interest will focus on the scaling regime that develops at long times after the
quench. How can one determine the growth laws that describe the time-dependence
of characteristic length scales, and what can be said about the form of the
associated scaling functions? Particular attention will be paid to systems
described by more complicated order parameters than the simple scalars usually
considered, e.g. vector and tensor fields. The latter are needed, for example,
to describe phase ordering in nematic liquid crystals, on which there have been
a number of recent experiments. The study of topological defects (domain walls,
vortices, strings, monopoles) provides a unifying framework for discussing
coarsening in these different systems.Comment: To appear in Advances in Physics. 85 pages, latex, no figures. For a
hard copy with figures, email [email protected]
Quantum critical point and scaling in a layered array of ultrasmall Josephson junctions
We have studied a quantum Hamiltonian that models an array of ultrasmall
Josephson junctions with short range Josephson couplings, , and charging
energies, , due to the small capacitance of the junctions. We derive a new
effective quantum spherical model for the array Hamiltonian. As an application
we start by approximating the capacitance matrix by its self-capacitive limit
and in the presence of an external uniform background of charges, . In
this limit we obtain the zero-temperature superconductor-insulator phase
diagram, , that improves upon previous theoretical
results that used a mean field theory approximation. Next we obtain a
closed-form expression for the conductivity of a square array, and derive a
universal scaling relation valid about the zero--temperature quantum critical
point. In the latter regime the energy scale is determined by temperature and
we establish universal scaling forms for the frequency dependence of the
conductivity.Comment: 18 pages, four Postscript figures, REVTEX style, Physical Review B
1999. We have added one important reference to this version of the pape
Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics
We extend the exact multilocal renormalization group (RG) method to study the
flow of the effective action functional. This important physical quantity
satisfies an exact RG equation which is then expanded in multilocal components.
Integrating the nonlocal parts yields a closed exact RG equation for the local
part, to a given order in the local part. The method is illustrated on the O(N)
model by straightforwardly recovering the exponent and scaling
functions. Then it is applied to study the glass phase of the Cardy-Ostlund,
random phase sine Gordon model near the glass transition temperature. The
static correlations and equilibrium dynamical exponent are recovered and
several new results are obtained. The equilibrium two-point scaling functions
are obtained. The nonequilibrium, finite momentum, two-time response and
correlations are computed. They are shown to exhibit scaling forms,
characterized by novel exponents , as well as
universal scaling functions that we compute. The fluctuation dissipation ratio
is found to be non trivial and of the form . Analogies and
differences with pure critical models are discussed.Comment: 33 pages, RevTe