21,797 research outputs found
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
Critical behavior of dissipative two-dimensional spin lattices
We explore critical properties of two-dimensional lattices of spins
interacting via an anisotropic Heisenberg Hamiltonian and subject to incoherent
spin flips. We determine the steady-state solution of the master equation for
the density matrix via the corner-space renormalization method. We investigate
the finite-size scaling and critical exponent of the magnetic linear
susceptibility associated to a dissipative ferromagnetic transition. We show
that the Von Neumann entropy increases across the critical point, revealing a
strongly mixed character of the ferromagnetic phase. Entanglement is witnessed
by the quantum Fisher information which exhibits a critical behavior at the
transition point, showing that quantum correlations play a crucial role in the
transition even though the system is in a mixed state.Comment: Accepted for publication on Phys. Rev. B (6 pages, 5 figures
Finite-Size Corrections for Ground States of Edwards-Anderson Spin Glasses
Extensive computations of ground state energies of the Edwards-Anderson spin
glass on bond-diluted, hypercubic lattices are conducted in dimensions
d=3,..,7. Results are presented for bond-densities exactly at the percolation
threshold, p=p_c, and deep within the glassy regime, p>p_c, where finding
ground-states becomes a hard combinatorial problem. Finite-size corrections of
the form 1/N^w are shown to be consistent throughout with the prediction
w=1-y/d, where y refers to the "stiffness" exponent that controls the formation
of domain wall excitations at low temperatures. At p=p_c, an extrapolation for
appears to match our mean-field results for these corrections. In
the glassy phase, w does not approach the value of 2/3 for large d predicted
from simulations of the Sherrington-Kirkpatrick spin glass. However, the value
of w reached at the upper critical dimension does match certain mean-field spin
glass models on sparse random networks of regular degree called Bethe lattices.Comment: 6 pages, RevTex4, all ps figures included, corrected and final
version with extended analysis and more data, such as for case d=3. Find
additional information at http://www.physics.emory.edu/faculty/boettcher
Interface Energy in the Edwards-Anderson model
We numerically investigate the spin glass energy interface problem in three
dimensions. We analyze the energy cost of changing the overlap from -1 to +1 at
one boundary of two coupled systems (in the other boundary the overlap is kept
fixed to +1). We implement a parallel tempering algorithm that simulate finite
temperature systems and work with both cubic lattices and parallelepiped with
fixed aspect ratio. We find results consistent with a lower critical dimension
. The results show a good agreement with the mean field theory
predictions.Comment: 5 pages; 7 figures; corrected typos; to appear in JS
Finite time and asymptotic behaviour of the maximal excursion of a random walk
We evaluate the limit distribution of the maximal excursion of a random walk
in any dimension for homogeneous environments and for self-similar supports
under the assumption of spherical symmetry. This distribution is obtained in
closed form and is an approximation of the exact distribution comparable to
that obtained by real space renormalization methods. Then we focus on the early
time behaviour of this quantity. The instantaneous diffusion exponent
exhibits a systematic overshooting of the long time exponent. Exact results are
obtained in one dimension up to third order in . In two dimensions,
on a regular lattice and on the Sierpi\'nski gasket we find numerically that
the analytic scaling holds.Comment: 9 pages, 4 figures, accepted J. Phys.
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