Zero-Temperature Dynamics of theS=12Linear Heisenberg Antiferromagnet

1979 ◽  
Vol 43 (1) ◽  
pp. 75-78 ◽  
Author(s):  
Gerhard Müller ◽  
Hans Beck ◽  
Jill C. Bonner
Keyword(s):  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
Temperature Dynamics

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.

scholarly journals EMPTINESS FORMATION PROBABILITY AND QUANTUM KNIZHNIK-ZAMOLODCHIKOV EQUATION

2004 ◽  
Vol 19 (supp02) ◽  
pp. 57-81
Author(s):  
H. E. BOOS ◽  
V. E. KOREPIN ◽  
F. A. SMIRNOV
Keyword(s):  
Quantum Correlations ◽  
Zero Magnetic Field ◽  
Heisenberg Antiferromagnet ◽  
Zero Temperature ◽  
One Dimensional ◽  
Formation Probability ◽  
Antiferromagnetic Ground State ◽  
A New Technique ◽  
The One ◽  
Zamolodchikov Equation

We consider the one-dimensional XXX spin 1/2 Heisenberg antiferromagnet at zero temperature and zero magnetic field. We are interested in a probability of a formation of a ferromagnetic string P(n) in the antiferromagnetic ground-state. We call it emptiness formation probability [EFP]. We suggest a new technique for computation of the EFP in the inhomogeneous case. It is based on the quantum Knizhnik-Zamolodchikov equation [qKZ]. We calculate EFP for n≤6 for the inhomogeneous case. The homogeneous limit confirms our hypothesis about the relation of quantum correlations and number theory. We also make a conjecture about a structure of EFP for arbrary n.

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