2,640 research outputs found
On Witten multiple zeta-functions associated with semisimple Lie algebras IV
In our previous work, we established the theory of multi-variable Witten
zeta-functions, which are called the zeta-functions of root systems. We have
already considered the cases of types , , , and . In
this paper, we consider the case of -type. We define certain analogues of
Bernoulli polynomials of -type and study the generating functions of them
to determine the coefficients of Witten's volume formulas of -type. Next
we consider the meromorphic continuation of the zeta-function of -type and
determine its possible singularities. Finally, by using our previous method, we
give explicit functional relations for them which include Witten's volume
formulas.Comment: 22 pag
Functional relations for zeta-functions of weight lattices of Lie groups of type
We study zeta-functions of weight lattices of compact connected semisimple
Lie groups of type . Actually we consider zeta-functions of SU(4), SO(6)
and PU(4), and give some functional relations and new classes of evaluation
formulas for them.Comment: 25 Page
Real space application of the mean-field description of spin glass dynamics
The out of equilibrium dynamics of finite dimensional spin glasses is
considered from a point of view going beyond the standard `mean-field theory'
versus `droplet picture' debate of the last decades. The main predictions of
both theories concerning the spin glass dynamics are discussed. It is shown, in
particular, that predictions originating from mean-field ideas concerning the
violations of the fluctuation-dissipation theorem apply quantitatively,
provided one properly takes into account the role of the spin glass coherence
length which plays a central role in the droplet picture. Dynamics in a uniform
magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio
Field-Shift Aging Protocol on the 3D Ising Spin-Glass Model: Dynamical Crossover between the Spin-Glass and Paramagnetic States
Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model
under a static magnetic field are examined by means of the standard Monte
Carlo simulation on the field-shift aging protocol at temperature . For each
process with (T; \tw, h), \tw being the waiting time before the field is
switched on, we extract the dynamical crossover time, \tcr(T; \tw, h). We
have found a nice scaling relation between the two characteristic length scales
which are properly determined from \tcr and \tw and then are normalized by
the static field crossover length introduced in the SG droplet theory. This
scaling behavior implies the instability of the SG phase in the equilibrium
limit even under an infinitesimal . In comparison with this numerical result
the field effect on real spin glasses is also discussed.Comment: 4 pages, 5 figures, jpsj2, Changed conten
Time and length scales in spin glasses
We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy
phase. We briefly review the present theoretical understanding of the
spectacular phenomena observed in experiments and describe new numerical
results obtained in the first large-scale simulation of the nonequilibrium
dynamics of the three dimensional Heisenberg spin glass.Comment: Paper presented at "Highly Frustrated Magnetism 2003", Grenoble,
August 200
Symmetrical Temperature-Chaos Effect with Positive and Negative Temperature Shifts in a Spin Glass
The aging in a Heisenberg-like spin glass Ag(11 at% Mn) is investigated by
measurements of the zero field cooled magnetic relaxation at a constant
temperature after small temperature shifts . A
crossover from fully accumulative to non-accumulative aging is observed, and by
converting time scales to length scales using the logarithmic growth law of the
droplet model, we find a quantitative evidence that positive and negative
temperature shifts cause an equivalent restart of aging (rejuvenation) in terms
of dynamical length scales. This result supports the existence of a unique
overlap length between a pair of equilibrium states in the spin glass system.Comment: 4 page
Aging dynamics in reentrant ferromagnet: CuCoCl-FeCl graphite bi-intercalation compound
Aging dynamics of a reentrant ferromagnet
CuCoCl-FeCl graphite bi-intercalation compound has
been studied using AC and DC magnetic susceptibility. This compound undergoes
successive transitions at the transition temperatures ( K) and
( K). The relaxation rate exhibits a characteristic
peak at close to a wait time below , indicating that
the aging phenomena occur in both the reentrant spin glass (RSG) phase below
and the ferromagnetic (FM) phase between and . The
relaxation rate () in the FM phase
exhibits two peaks around and a time much shorter than under
the positive -shift aging, indicating a partial rejuvenation of domains. The
aging state in the FM phase is fragile against a weak magnetic-field
perturbation. The time () dependence of around is well approximated by a stretched exponential relaxation:
. The exponent depends on
, , and . The relaxation time () exhibits a
local maximum around 5 K, reflecting a chaotic nature of the FM phase. It
drastically increases with decreasing temperature below .Comment: 16 pages,16 figures, submitted to Physical Review
A generalized Macdonald operator
We present an explicit difference operator diagonalized by the Macdonald
polynomials associated with an (arbitrary) admissible pair of irreducible
reduced crystallographic root systems. By the duality symmetry, this gives rise
to an explicit Pieri formula for the Macdonald polynomials in question. The
simplest examples of our construction recover Macdonald's celebrated difference
operators and associated Pieri formulas pertaining to the minuscule and
quasi-minuscule weights. As further by-products, explicit expansions and
Littlewood-Richardson type formulas are obtained for the Macdonald polynomials
associated with a special class of small weights.Comment: 11 pages. To appear in Int. Math. Res. Not. IMR
Temperature Chaos, Rejuvenation and Memory in Migdal-Kadanoff Spin Glasses
We use simulations within the Migdal-Kadanoff real space renormalization
approach to probe the scales relevant for rejuvenation and memory in spin
glasses. One of the central questions concerns the role of temperature chaos.
First we investigate scaling laws of equilibrium temperature chaos, finding
super-exponential decay of correlations but no chaos for the total free energy.
Then we perform out of equilibrium simulations that follow experimental
protocols. We find that: (1) rejuvenation arises at a length scale smaller than
the ``overlap length'' l(T,T'); (2) memory survives even if equilibration goes
out to length scales much larger than l(T,T').Comment: 4 pages, 4 figures, added references, slightly changed content,
modified Fig.
Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function
Using Monte Carlo simulations, we have studied isothermal aging of
three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior
of the spin auto-correlation function. Weak violation of the time translational
invariance in the quasi-equilibrium regime is analyzed in terms of {\it
effective stiffness} for droplet excitations in the presence of domain walls.
Within the range of computational time window, we have confirmed that the
effective stiffness follows the expected scaling behavior with respect to the
characteristic length scales associated with droplet excitations and domain
walls, whose growth law has been extracted from our simulated data. Implication
of the results are discussed in relation to experimental works on ac
susceptibilities.Comment: 18 pages, 6 figure
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