scholarly journals ON THE STATISTICAL PROPERTIES OF THE LARGE TIME ZERO TEMPERATURE DYNAMICS OF THE SK MODEL

2002 ◽  
Author(s):  
GIORGIO PARISI
Keyword(s):  
Large Time ◽  
Statistical Properties ◽  
Zero Temperature ◽  
Time Zero ◽  
Temperature Dynamics

scholarly journals ON THE STATISTICAL PROPERTIES OF THE LARGE TIME ZERO TEMPERATURE DYNAMICS OF THE SK MODEL

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 161-171 ◽  
Author(s):  
GIORGIO PARISI
Keyword(s):  
Large Time ◽  
Weak Sense ◽  
Statistical Properties ◽  
Time Limit ◽  
Zero Temperature ◽  
Replica Symmetry ◽  
Equilibrium Dynamics ◽  
Temperature Dynamics ◽  
Kirkpatrick Model ◽  
Large Time Limit

Here we study the zero temperature dynamics of the Sherrington Kirkpatrick model and we investigate the statistical properties of the configurations that are obtained in the large time limit. We find that the replica symmetry is broken (in a weak sense). We also present some general considerations on the synchronic approach to the off-equilibrium dynamics, that has motivated the present study.

scholarly journals EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES

1996 ◽  
Vol 10 (25) ◽  
pp. 3451-3459 ◽  
Author(s):  
ANTÓNIO M.R. CADILHE ◽  
VLADIMIR PRIVMAN
Keyword(s):  
Exact Solution ◽  
Domain Wall ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Initial Conditions ◽  
Strong Dependence ◽  
Zero Temperature ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Dynamics

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins ↑↓ (↓↑) can exchange to assume the configuration ↓↑ (↑↓), with rate β(α), through energy decreasing moves only. We report exact solution for the case when one of the rates, α or β, is zero. The irreversibility of such zero-temperature dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general, finite-temperature models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.

scholarly journals PERSISTENCE IN THE ZERO-TEMPERATURE DYNAMICS OF THE Q-STATES POTTS MODEL ON UNDIRECTED-DIRECTED BARABÁSI–ALBERT NETWORKS AND ERDÖS–RÉNYI RANDOM GRAPHS

2008 ◽  
Vol 19 (12) ◽  
pp. 1777-1785 ◽  
Author(s):  
F. P. FERNANDES ◽  
F. W. S. LIMA
Keyword(s):  
Random Graphs ◽  
Potts Model ◽  
Finite Size ◽  
Glauber Dynamics ◽  
The Other ◽  
Finite Size Effect ◽  
Zero Temperature ◽  
Temperature Dynamics ◽  
Short Times ◽  
Q Values

The zero-temperature Glauber dynamics is used to investigate the persistence probability P(t) in the Potts model with Q = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16 384, …, 230 states on directed and undirected Barabási–Albert networks and Erdös–Rényi (ER) random graphs. In this model, it is found that P(t) decays exponentially to zero in short times for directed and undirected ER random graphs. For directed and undirected BA networks, in contrast it decays exponentially to a constant value for long times, i.e., P(∞) is different from zero for all Q values (here studied) from Q = 3, 4, 5, …, 230; this shows "blocking" for all these Q values. Except that for Q = 230 in the undirected case P(t) tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.

ON THE STABILIZATION OF A VISCOUS BAROTROPIC SELF-GRAVITATING MEDIUM WITH A NONMONOTONE EQUATION OF STATE

2002 ◽  
Vol 12 (01) ◽  
pp. 143-153 ◽  
Author(s):  
B. DUCOMET ◽  
A. A. ZLOTNIK
Keyword(s):  
Equation Of State ◽  
Stokes System ◽  
Large Time ◽  
Asymptotic Properties ◽  
One Dimension ◽  
Navier Stokes ◽  
Zero Temperature ◽  
Quantum Fluid ◽  
Coulomb Effects ◽  
Nonmonotone Equation

We consider the compressible barotropic Navier–Stokes system in one dimension, with a nonmonotone equation of state and self-gravitation. We solve an associated "fixed-free" boundary problem and prove asymptotic properties of the unique globally defined solution for large time. We also comment on a related model of quantum fluid describing the dynamics of nuclear matter with zero temperature and Coulomb effects.

On the range of a constrained random walk

1988 ◽  
Vol 25 (03) ◽  
pp. 451-463
Author(s):  
W. Th. F. Den Hollander ◽  
G. H. Weiss
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Large Time ◽  
Statistical Properties ◽  
Time Limit ◽  
The Mean ◽  
Large Time Limit ◽  
Lattice Random Walk

We study statistical properties of the range (= number of distinct sites visited) of a lattice random walk in discrete time constrained to visit a given site at a given time. In particular, we calculate the mean and obtain a bound on the variance of the range in the large time limit. The results are applied to a problem involving an unconstrained random walk in the presence of randomly distributed traps. A key role is played by the associated random walk that is obtained from the original random walk via a Cramer transform.

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