59 research outputs found
The staggered domain wall fermion method
A different lattice fermion method is introduced. Staggered domain wall
fermions are defined in 2n+1 dimensions and describe 2^n flavors of light
lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As
the size of the extra dimension becomes large, 2^n chiral flavors with the same
chiral charge are expected to be localized on each boundary and the full
SU(2^n) x SU(2^n) flavor chiral symmetry is expected to be recovered. SDWF give
a different perspective into the inherent flavor mixing of lattice fermions and
by design present an advantage for numerical simulations of lattice QCD
thermodynamics. The chiral and topological index properties of the SDWF Dirac
operator are investigated. And, there is a surprise ending...Comment: revtex4, 7 figures, minor revisions, 2 references adde
Magnetoresistance of Three-Constituent Composites: Percolation Near a Critical Line
Scaling theory, duality symmetry, and numerical simulations of a random
network model are used to study the magnetoresistance of a
metal/insulator/perfect conductor composite with a disordered columnar
microstructure. The phase diagram is found to have a critical line which
separates regions of saturating and non-saturating magnetoresistance. The
percolation problem which describes this line is a generalization of
anisotropic percolation. We locate the percolation threshold and determine the
t = s = 1.30 +- 0.02, nu = 4/3 +- 0.02, which are the same as in
two-constituent 2D isotropic percolation. We also determine the exponents which
characterize the critical dependence on magnetic field, and confirm numerically
that nu is independent of anisotropy. We propose and test a complete scaling
description of the magnetoresistance in the vicinity of the critical line.Comment: Substantially revised version; description of behavior in finite
magnetic fields added. 7 pages, 7 figures, submitted to PR
Magnetic order in the Ising model with parallel dynamics
It is discussed how the equilibrium properties of the Ising model are
described by an Hamiltonian with an antiferromagnetic low temperature behavior
if only an heat bath dynamics, with the characteristics of a Probabilistic
Cellular Automaton, is assumed to determine the temporal evolution of the
system.Comment: 9 pages, 3 figure
On the study of jamming percolation
We investigate kinetically constrained models of glassy transitions, and
determine which model characteristics are crucial in allowing a rigorous proof
that such models have discontinuous transitions with faster than power law
diverging length and time scales. The models we investigate have constraints
similar to that of the knights model, introduced by Toninelli, Biroli, and
Fisher (TBF), but differing neighbor relations. We find that such knights-like
models, otherwise known as models of jamming percolation, need a ``No Parallel
Crossing'' rule for the TBF proof of a glassy transition to be valid.
Furthermore, most knight-like models fail a ``No Perpendicular Crossing''
requirement, and thus need modification to be made rigorous. We also show how
the ``No Parallel Crossing'' requirement can be used to evaluate the provable
glassiness of other correlated percolation models, by looking at models with
more stable directions than the knights model. Finally, we show that the TBF
proof does not generalize in any straightforward fashion for three-dimensional
versions of the knights-like models.Comment: 13 pages, 18 figures; Spiral model does satisfy property
Fermion-scalar interactions with domain wall fermions
Domain wall fermions are defined on a lattice with an extra direction the
size of which controls the chiral properties of the theory. When gauge fields
are coupled to domain wall fermions the extra direction is treated as an
internal flavor space. Here it is found that this is not the case for scalar
fields. Instead, the interaction takes place only along the link that connects
the boundaries of the extra direction. This reveals a richness in the way
different spin particles are coupled to domain wall fermions. As an
application, 4-Fermi models are studied using large N techniques and the
results are supported by numerical simulations with N=2. It is found that the
chiral properties of domain wall fermions in these models are good across a
large range of couplings and that a phase with parity-flavor broken symmetry
can develop for negative bare masses if the number of sites along the extra
direction is finite.Comment: LaTeX, 17 pages, 8 eps figures; comment regarding the width of Aoki
phase added in sec. 3; references adde
Crossover behavior of the J1-J2 model in a staggered magnetic field
The ground states of the Heisenberg chain with the
nearest-neighbor and the next-nearest-neighbor antiferromagnetic couplings are
numerically investigated in a staggered magnetic field. While the staggered
magnetic field may induce the N\'eel-type excitation gap, and it is
characterized by the Gaussian fixed point in the spin-fluid region, the
crossover to the behavior controlled by the Ising fixed point is expected to be
observed for the spontaneously dimerized state at finite field. Treating a
low-lying excitation gap by the phenomenological renormalization-group method,
we numerically determine the massless flow connecting the Gaussian and Ising
fixed points. Further, to check the criticalities, we perform the
finite-size-scaling analysis of the excitation gap.Comment: 4 pages, 3 figure
On the nature of the finite-temperature transition in QCD
We discuss the nature of the finite-temperature transition in QCD with N_f
massless flavors. Universality arguments show that a continuous (second-order)
transition must be related to a 3-D universality class characterized by a
complex N_f X N_f matrix order parameter and by the symmetry-breaking pattern
[SU(N_f)_L X SU(N_f)_R]/Z(N_f)_V -> SU(N_f)_V/Z(N_f)_V, or [U(N_f)_L X
U(N_f)_R]/U(1)_V -> U(N_f)_V/U(1)_V if the U(1)_A symmetry is effectively
restored at T_c. The existence of any of these universality classes requires
the presence of a stable fixed point in the corresponding 3-D Phi^4 theory with
the expected symmetry-breaking pattern. Otherwise, the transition is of first
order. In order to search for stable fixed points in these Phi^4 theories, we
exploit a 3-D perturbative approach in which physical quantities are expanded
in powers of appropriate renormalized quartic couplings. We compute the
corresponding Callan-Symanzik beta-functions to six loops. We also determine
the large-order behavior to further constrain the analysis. No stable fixed
point is found, except for N_f=2, corresponding to the symmetry-breaking
pattern [SU(2)_L X SU(2)_R]/Z(2)_V -> SU(2)_V/Z(2)_V equivalent to O(4) ->
O(3). Our results confirm and put on a firmer ground earlier analyses performed
close to four dimensions, based on first-order calculations in the framework of
the epsilon=4-d expansion. These results indicate that the finite-temperature
phase transition in QCD is of first order for N_f>2. A continuous transition is
allowed only for N_f=2. But, since the theory with symmetry-breaking pattern
[U(2)_L X U(2)_R]/U(1)_V -> U(2)_V/U(1)_V does not have stable fixed points,
the transition can be continuous only if the effective breaking of the U(1)_A
symmetry is sufficiently large.Comment: 30 pages, 3 figs, minor correction
Topology and Computational Performance of Attractor Neural Networks
To explore the relation between network structure and function, we studied
the computational performance of Hopfield-type attractor neural nets with
regular lattice, random, small-world and scale-free topologies. The random net
is the most efficient for storage and retrieval of patterns by the entire
network. However, in the scale-free case retrieval errors are not distributed
uniformly: the portion of a pattern encoded by the subset of highly connected
nodes is more robust and efficiently recognized than the rest of the pattern.
The scale-free network thus achieves a very strong partial recognition.
Implications for brain function and social dynamics are suggestive.Comment: 2 figures included. Submitted to Phys. Rev. Letter
The finite-temperature chiral transition in QCD with adjoint fermions
We study the nature of the finite-temperature chiral transition in QCD with
N_f light quarks in the adjoint representation (aQCD). Renormalization-group
arguments show that the transition can be continuous if a stable fixed point
exists in the renormalization-group flow of the corresponding three-dimensional
Phi^4 theory with a complex 2N_f x 2N_f symmetric matrix field and
symmetry-breaking pattern SU(2N_f)->SO(2N_f). This issue is investigated by
exploiting two three-dimensional perturbative approaches, the massless
minimal-subtraction scheme without epsilon expansion and a massive scheme in
which correlation functions are renormalized at zero momentum. We compute the
renormalization-group functions in the two schemes to five and six loops
respectively, and determine their large-order behavior.
The analyses of the series show the presence of a stable three-dimensional
fixed point characterized by the symmetry-breaking pattern SU(4)->SO(4). This
fixed point does not appear in an epsilon-expansion analysis and therefore does
not exist close to four dimensions. The finite-temperature chiral transition in
two-flavor aQCD can therefore be continuous; in this case its critical behavior
is determined by this new SU(4)/SO(4) universality class. One-flavor aQCD may
show a more complex phase diagram with two phase transitions. One of them, if
continuous, should belong to the O(3) vector universality class.Comment: 36 page
Segregated tunneling-percolation model for transport nonuniversality
We propose a theory of the origin of transport nonuniversality in disordered
insulating-conducting compounds based on the interplay between microstructure
and tunneling processes between metallic grains dispersed in the insulating
host. We show that if the metallic phase is arranged in quasi-one dimensional
chains of conducting grains, then the distribution function of the chain
conductivities g has a power-law divergence for g -> 0 leading to nonuniversal
values of the transport critical exponent t. We evaluate the critical exponent
t by Monte Carlo calculations on a cubic lattice and show that our model can
describe universal as well nonuniversal behavior of transport depending on the
value of few microstructural parameters. Such segregated tunneling-percolation
model can describe the microstructure of a quite vast class of materials known
as thick-film resistors which display universal or nonuniversal values of t
depending on the composition.Comment: 8 pages, 5 figures (Phys. Rev. B - 1 August 2003)(fig1 replaced
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