127 research outputs found
Jarzynski Equality for an Energy-Controlled System
The Jarzynski equality (JE) is known as an exact identity for nonequillibrium
systems. The JE was originally formulated for isolated and isothermal systems,
while Adib reported an JE extended to an isoenergetic process. In this paper,
we extend the JE to an energy-controlled system. We make it possible to control
the instantaneous value of the energy arbitrarily in a nonequilibrium process.
Under our extension, the new JE is more practical and useful to calculate the
number of states and the entropy than the isoenergetic one. We also show
application of our JE to a kind of optimization problems.Comment: 6 pages, 1 figur
Analytical evidence for the absence of spin glass transition on self-dual lattices
We show strong evidence for the absence of a finite-temperature spin glass
transition for the random-bond Ising model on self-dual lattices. The analysis
is performed by an application of duality relations, which enables us to derive
a precise but approximate location of the multicritical point on the Nishimori
line. This method can be systematically improved to presumably give the exact
result asymptotically. The duality analysis, in conjunction with the
relationship between the multicritical point and the spin glass transition
point for the symmetric distribution function of randomness, leads to the
conclusion of the absence of a finite-temperature spin glass transition for the
case of symmetric distribution. The result is applicable to the random bond
Ising model with or Gaussian distribution and the Potts gauge glass on
the square, triangular and hexagonal lattices as well as the random three-body
Ising model on the triangular and the Union-Jack lattices and the four
dimensional random plaquette gauge model. This conclusion is exact provided
that the replica method is valid and the asymptotic limit of the duality
analysis yields the exact location of the multicritical pointComment: 11 Pages, 4 figures, 1 table. submitted to J. Phys. A Math. Theo
Universality in phase boundary slopes for spin glasses on self dual lattices
We study the effects of disorder on the slope of the disorder--temperature
phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So
far, studies have focused on marginal or irrelevant cases of disorder. Using
duality arguments, as well as exact Pfaffian techniques we reproduce these
analytical estimates. In addition, we obtain different estimates for spin-glass
models on hierarchical lattices where the effects of disorder are relevant. We
show that the phase-boundary slope near the Onsager point can be used to probe
for the relevance of disorder effects.Comment: 8 pages, 6 figure
The nature of the different zero-temperature phases in discrete two-dimensional spin glasses: Entropy, universality, chaos and cascades in the renormalization group flow
The properties of discrete two-dimensional spin glasses depend strongly on
the way the zero-temperature limit is taken. We discuss this phenomenon in the
context of the Migdal-Kadanoff renormalization group. We see, in particular,
how these properties are connected with the presence of a cascade of fixed
points in the renormalization group flow. Of particular interest are two
unstable fixed points that correspond to two different spin-glass phases at
zero temperature. We discuss how these phenomena are related with the presence
of entropy fluctuations and temperature chaos, and universality in this model.Comment: 14 pages, 5 figures, 2 table
Multicritical Points of Potts Spin Glasses on the Triangular Lattice
We predict the locations of several multicritical points of the Potts spin
glass model on the triangular lattice. In particular, continuous multicritical
lines, which consist of multicritical points, are obtained for two types of
two-state Potts (i.e., Ising) spin glasses with two- and three-body
interactions on the triangular lattice. These results provide us with numerous
examples to further verify the validity of the conjecture, which has succeeded
in deriving highly precise locations of multicritical points for several spin
glass models. The technique, called the direct triangular duality, a variant of
the ordinary duality transformation, directly relates the triangular lattice
with its dual triangular lattice in conjunction with the replica method.Comment: 18 pages, 2, figure
CENP-C and CENP-I are key connecting factors for kinetochore and CENP-A assembly
Although it is generally accepted that chromatin containing the histone H3 variant CENP-A is an epigenetic mark maintaining centromere identity, the pathways leading to the formation and maintenance of centromere chromatin remain unclear. We previously generated human artificial chromosomes (HACs) whose centromeres contain a synthetic alpha-satellite (alphoid) DNA array containing the tetracycline operator (alphoid(tetO)). We also obtained cell lines bearing the alphoid(tetO) array at ectopic integration sites on chromosomal arms. Here, we have examined the regulation of CENP-A assembly at centromeres as well as de novo assembly on the ectopic arrays by tethering tetracycline repressor (tetR) fusions of substantial centromeric factors and chromatin modifiers. This analysis revealed four classes of factors that influence CENP-A assembly. Interestingly, many kinetochore structural components induced de novo CENP-A assembly at the ectopic site. We showed that these components work by recruiting CENP-C and subsequently recruiting M18BP1. Furthermore, we found that CENP-I can also recruit M18BP1 and, as a consequence, enhances M18BP1 assembly on centromeres in the downstream of CENP-C. Thus, we suggest that CENP-C and CENP-I are key factors connecting kinetochore to CENP-A assembly
Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
Topological color codes are among the stabilizer codes with remarkable
properties from quantum information perspective. In this paper we construct a
four-valent lattice, the so called ruby lattice, governed by a 2-body
Hamiltonian. In a particular regime of coupling constants, degenerate
perturbation theory implies that the low energy spectrum of the model can be
described by a many-body effective Hamiltonian, which encodes the color code as
its ground state subspace. The gauge symmetry
of color code could already be realized by
identifying three distinct plaquette operators on the lattice. Plaquettes are
extended to closed strings or string-net structures. Non-contractible closed
strings winding the space commute with Hamiltonian but not always with each
other giving rise to exact topological degeneracy of the model. Connection to
2-colexes can be established at the non-perturbative level. The particular
structure of the 2-body Hamiltonian provides a fruitful interpretation in terms
of mapping to bosons coupled to effective spins. We show that high energy
excitations of the model have fermionic statistics. They form three families of
high energy excitations each of one color. Furthermore, we show that they
belong to a particular family of topological charges. Also, we use
Jordan-Wigner transformation in order to test the integrability of the model
via introducing of Majorana fermions. The four-valent structure of the lattice
prevents to reduce the fermionized Hamiltonian into a quadratic form due to
interacting gauge fields. We also propose another construction for 2-body
Hamiltonian based on the connection between color codes and cluster states. We
discuss this latter approach along the construction based on the ruby lattice.Comment: 56 pages, 16 figures, published version
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