367 research outputs found

### The wormhole move: A new algorithm for polymer simulations

A new Monte Carlo move for polymer simulations is presented. The ``wormhole''
move is build out of reptation steps and allows a polymer to reptate through a
hole in space; it is able to completely displace a polymer in time N^2 (with N
the polymer length) even at high density. This move can be used in a similar
way to configurational bias, in particular it allows grand canonical moves, it
is applicable to copolymers and can be extended to branched polymers. The main
advantage is speed since it is exponentially faster in N than configurational
bias, but is also easier to program.Comment: 8 pages, 6 figure

### A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The
use of clusters makes possible global updates and leads to a gain in speed of
several orders of magnitude. As an example, we study the 2-dimensional +/-J
Edwards-Anderson model. The new algorithm allows us to equilibrate systems of
size 100^2 down to temperature T = 0.1. Our main result is that the correlation
length diverges as an exponential and not as a power law as T -> Tc = 0.Comment: 6 pages, 9 figures, section 2 completly rewritte

### Reply to Comment on "Ising Spin Glasses in a Magnetic Field"

The problem of the survival of a spin glass phase in the presence of a field
has been a challenging one for a long time. To date, all attempts using
equilibrium Monte Carlo methods have been unconclusive. In their comment to our
paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test
for an Almeida-Thouless line. In our view such a dynamic approach is not based
on very solid foundations in finite dimensional systems and so cannot be as
compelling as equilibrium approaches. Nevertheless, the results of those
authors suggests that there is a critical field near B=0.4 at zero temperature.
In view of this quite small value (compared to the mean field value), we have
reanalyzed our data. We find that if finite size scaling is to distinguish
between that small field and a zero field, we would need to go to lattice sizes
of about 20x20x20.Comment: reply to comment cond-mat/9812401 on ref. cond-mat/981141

### A geometrical picture for finite dimensional spin glasses

A controversial issue in spin glass theory is whether mean field correctly
describes 3-dimensional spin glasses. If it does, how can replica symmetry
breaking arise in terms of spin clusters in Euclidean space? Here we argue that
there exist system-size low energy excitations that are sponge-like, generating
multiple valleys separated by diverging energy barriers. The droplet model
should be valid for length scales smaller than the size of the system (theta >
0), but nevertheless there can be system-size excitations of constant energy
without destroying the spin glass phase. The picture we propose then combines
droplet-like behavior at finite length scales with a potentially mean field
behavior at the system-size scale.Comment: 7 pages; modified references, clarifications; to appear in EP

### Low-temperature behavior of two-dimensional Gaussian Ising spin glasses

We perform Monte Carlo simulations of large two-dimensional Gaussian Ising
spin glasses down to very low temperatures $\beta=1/T=50$. Equilibration is
ensured by using a cluster algorithm including Monte Carlo moves consisting of
flipping fundamental excitations. We study the thermodynamic behavior using the
Binder cumulant, the spin-glass susceptibility, the distribution of overlaps,
the overlap with the ground state and the specific heat. We confirm that
$T_c=0$. All results are compatible with an algebraic divergence of the
correlation length with an exponent $\nu$. We find $-1/\nu=-0.295(30)$, which
is compatible with the value for the domain-wall and droplet exponent
$\theta\approx-0.29$ found previously in ground-state studies. Hence the
thermodynamic behavior of this model seems to be governed by one single
exponent.Comment: 7 pages, 11 figure

### Dipolar SLEs

We present basic properties of Dipolar SLEs, a new version of stochastic
Loewner evolutions (SLE) in which the critical interfaces end randomly on an
interval of the boundary of a planar domain. We present a general argument
explaining why correlation functions of models of statistical mechanics are
expected to be martingales and we give a relation between dipolar SLEs and
CFTs. We compute SLE excursion and/or visiting probabilities, including the
probability for a point to be on the left/right of the SLE trace or that to be
inside the SLE hull. These functions, which turn out to be harmonic, have a
simple CFT interpretation. We also present numerical simulations of the
ferromagnetic Ising interface that confirm both the probabilistic approach and
the CFT mapping.Comment: 22 pages, 4 figure

### Large-scale low-energy excitations in 3-d spin glasses

We numerically extract large-scale excitations above the ground state in the
3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that
associated energies are O(1), in agreement with the mean field picture. Of
further interest are the position-space properties of these excitations. First,
our study of their topological properties show that the majority of the
large-scale excitations are sponge-like. Second, when probing their geometrical
properties, we find that the excitations coarsen when the system size is
increased. We conclude that either finite size effects are very large even when
the spin overlap q is close to zero, or the mean field picture of homogeneous
excitations has to be modified.Comment: 11 pages, typos corrected, added reference

### Zero-temperature responses of a 3D spin glass in a field

We probe the energy landscape of the 3D Edwards-Anderson spin glass in a
magnetic field to test for a spin glass ordering. We find that the spin glass
susceptibility is anomalously large on the lattice sizes we can reach. Our data
suggest that a transition from the spin glass to the paramagnetic phase takes
place at B_c=0.65, though the possibility B_c=0 cannot be excluded. We also
discuss the question of the nature of the putative frozen phase.Comment: RevTex, 4 pages, 4 figures, clarifications and added reference

### Comparing Mean Field and Euclidean Matching Problems

Combinatorial optimization is a fertile testing ground for statistical
physics methods developed in the context of disordered systems, allowing one to
confront theoretical mean field predictions with actual properties of finite
dimensional systems. Our focus here is on minimum matching problems, because
they are computationally tractable while both frustrated and disordered. We
first study a mean field model taking the link lengths between points to be
independent random variables. For this model we find perfect agreement with the
results of a replica calculation. Then we study the case where the points to be
matched are placed at random in a d-dimensional Euclidean space. Using the mean
field model as an approximation to the Euclidean case, we show numerically that
the mean field predictions are very accurate even at low dimension, and that
the error due to the approximation is O(1/d^2). Furthermore, it is possible to
improve upon this approximation by including the effects of Euclidean
correlations among k link lengths. Using k=3 (3-link correlations such as the
triangle inequality), the resulting errors in the energy density are already
less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series
expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur

### Spin and link overlaps in 3-dimensional spin glasses

Excitations of three-dimensional spin glasses are computed numerically. We
find that one can flip a finite fraction of an LxLxL lattice with an O(1)
energy cost, confirming the mean field picture of a non-trivial spin overlap
distribution P(q). These low energy excitations are not domain-wall-like,
rather they are topologically non-trivial and they reach out to the boundaries
of the lattice. Their surface to volume ratios decrease as L increases and may
asymptotically go to zero. If so, link and window overlaps between the ground
state and these excited states become ``trivial''.Comment: Extra fits comparing TNT to mean field, summarized in a tabl

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