On the Integrability of Classical Ruijsenaars-Schneider Model of BC2BC_{2} Type

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found by solving the set of two functional equations.Comment: 10 pages, LaTeX2e, no figure

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 $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-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

Aging phenomena in spin glasses: theory, experiment, and simulation

We study numerically temperature-shift and field-shift aging protocols on the 3-dimensional (3D) Ising Edwards-Anderson (EA) spin-glass (SG) model focusing on respectively the temperature-chaos nature and the stability under a static field of the SG phase. The results of the latter strongly support the droplet theory which predicts the instability of the SG phase under the field. They are also discussed in relation with the experimental studies.Comment: 6 pages, 5 figures, submitted to ICM200

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

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 $h$ are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature $T$. 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 $h$. In comparison with this numerical result the field effect on real spin glasses is also discussed.Comment: 4 pages, 5 figures, jpsj2, Changed conten