18,800 research outputs found
New technique for replica symmetry breaking with application to the SK-model at and near T=0
We describe a novel method which allows the treatment of high orders of
replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly,
without a need for approximations or scaling assumptions. It yields the low
temperature order function q(a,T) in the full range and is
complete in the sense that all observables can be calculated from it. The
behavior of some observables and the finite RSB theory itself is analyzed as
one approaches continuous RSB. The validity and applicability of the
traditional continuous formulation is then scrutinized and a new continuous RSB
formulation is proposed
Replica Symmetry Breaking Instability in the 2D XY model in a random field
We study the 2D vortex-free XY model in a random field, a model for randomly
pinned flux lines in a plane. We construct controlled RG recursion relations
which allow for replica symmetry breaking (RSB). The fixed point previously
found by Cardy and Ostlund in the glass phase is {\it unstable} to RSB.
The susceptibility associated to infinitesimal RSB perturbation in the
high-temperature phase is found to diverge as
when . This provides analytical evidence that RSB occurs
in finite dimensional models. The physical consequences for the glass phase are
discussed.Comment: 8 pages, REVTeX, LPTENS-94/2
On a Dynamical-Like Replica-Symmetry-Breaking Scheme for the Spin Glass
Considering the unphysical result obtained in the calculation of the
free-energy cost for twisting the boundary conditions in a spin glass, we trace
it to the negative multiplicities associated with the Parisi replica-symmetry
breaking (RSB). We point out that a distinct RSB, that keeps positive
multiplicities, was proposed long ago, in the spirit of an ultra-long time
dynamical approach due to Sompolinsky. For an homogeneous bulk system, both RSB
schemes are known to yield identical free energies and observables. However,
using the dynamical RSB, we have recalculated the twist free energy at the
mean-field level. The free-energy cost of this twist is, as expected, positive
in that scheme, as it should be
Replica Symmetry Breaking in the Critical Behaviour of the Random Ferromagnet
We study the critical properties of the weakly disordered -component
random Heisenberg ferromagnet. It is shown that if the specific heat critical
exponent of the pure system is positive, the traditional renormalization group
(RG) flows at dimensions D=4-\e, which are usually considered as describing
the disorder-induced universal critical behavior, are {\it unstable} with
respect to replica symmetry breaking (RSB) potentials as found in spin glasses.
It is demonstrated that the RG flows involving RSB potentials lead to fixed
points which have the structure known as the 1 step RSB, and there exists a
whole spectrum of such fixed points. It is argued that spontaneous RSB can
occur due to the interactions of the fluctuating fields with the local
non-perturbative degrees of freedom coming from the multiple local minima
solutions of the mean-field equations. However, it is not clear whether or not
RSB occurs for infinitesimally weak disorder. Physical consequences of these
conclusions are discussed.Comment: 20 pages, late
Replica Symmetry Breaking and the Renormalization Group Theory of the Weakly Disordered Ferromagnet
We study the critical properties of the weakly disordered -component
ferromagnet in terms of the renormalization group (RG) theory generalized to
take into account the replica symmetry breaking (RSB) effects coming from the
multiple local minima solutions of the mean-field equations. It is shown that
for the traditional RG flows at dimensions , which are
usually considered as describing the disorder-induced universal critical
behavior, are unstable with respect to the RSB potentials as found in spin
glasses. It is demonstrated that for a general type of the Parisi RSB
structures there exists no stable fixed points, and the RG flows lead to the
{\it strong coupling regime} at the finite scale , where
is the small parameter describing the disorder. The physical concequences
of the obtained RG solutions are discussed. In particular, we argue, that
discovered RSB strong coupling phenomena indicate on the onset of a new spin
glass type critical behaviour in the temperature interval near . Possible relevance of the considered RSB effects for
the Griffith phase is also discussed.Comment: 32 pages, Late
One-step replica symmetry breaking solution for a highly asymmetric two-sublattice fermionic Ising spin glass model in a transverse field
The one-step replica symmetry breaking (RSB) is used to study a
two-sublattice fermionic infinite-range Ising spin glass (SG) model in a
transverse field . The problem is formulated in a Grassmann path
integral formalism within the static approximation. In this model, a parallel
magnetic field breaks the symmetry of the sublattices. It destroys the
antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase
(SG+AF) characterizing an asymmetric RSB region. In this region,
intra-sublattice disordered interactions increase the difference between
the RSB solutions of each sublattice. The freezing temperature shows a higher
increase with when enhances. A discontinue phase transition from the
replica symmetry (RS) solution to the RSB solution can appear with the presence
of an intra-sublattice ferromagnetic average coupling. The field
introduces a quantum spin flip mechanism that suppresses the magnetic orders
leading them to quantum critical points. Results suggest that the quantum
effects are not able to restore the RS solution. However, in the asymmetric RSB
region, can produce a stable RS solution at any finite temperature for
a particular sublattice while the other sublattice still presents RSB solution
for the special case in which only the intra-sublattice spins couple with
disordered interactions.Comment: 11 pages, 8 figures, accepted for publication in Phys. Rev.
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