6 research outputs found
Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature
We analyze the replica-symmetry-breaking construction in the
Sherrington-Kirkpatrick model of a spin glass. We present a general scheme for
deriving an exact asymptotic behavior near the critical temperature of the
solution with an arbitrary number of discrete hierarchies of the broken replica
symmetry. We show that all solutions with finite-many hierarchies are unstable
and only the scheme with infinite-many hierarchies becomes marginally stable.
We show how the solutions from the discrete replica-symmetry-breaking scheme go
over to the continuous one with increasing the number of hierarchies.Comment: REVTeX4, 11 pages, no figure
Continuous RSB mean-field solution of the Potts glass
We investigate the p-state mean-field model of the
Potts glass () below the continuous phase transition to a
glassy phase. We find that apart from a solution with a first hierarchical
level of replica-symmetry breaking (1RSB), locally stable close to the
transition point, there is a continuous full replica-symmetry breaking (FRSB)
solution. The latter is marginally stable and has a higher free energy than the
former. We argue that the true equilibrium is reached only by FRSB, being
globally thermodynamically homogeneous, whereas 1RSB is only locally
homogeneous.Comment: REVTeX4.1, 4 pages, 1 figur
Zig-zag charged domain walls in ferroelectric PbTiO
We report a theoretical investigation of a charged 180 domain wall in
ferroelectric PbTiO, compensated by randomly distributed immobile charge
defects. For this we utilize atomistic shell-model simulations and continuous
phase-field simulations in the framework of the Ginzburg-Landau-Devonshire
model. We predict that domain walls form a zig-zag pattern and we discuss its
properties in a broad interval of compensation-region widths, ranging from a
couple to over a hundred nanometers