Ordering kinetics of the 2D qstate Potts model

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Ordering kinetics of the 2Dq-state Potts model

• Ezequiel E. Ferrero, Sergio A. Cannas
• and F. A. Tamarit
• Facultad de Matemática, Astronomía y Física
• Universidad Nacional de Córdoba
• Córdoba, Argentina

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Ferromagnetic q-state Potts Model
J gt 0

• 2nd order phase transition for q 2,3
• 1st order phase transition for q 4

2D ?
kB J 1
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Ordering kinetics Single spin-flip dynamics
Relaxation after a quench from T 8 to T lt Tc
for q gt 4
Monte Carlo simulations on a squares lattice with
N L x L sites (periodic boundary conditions)
for q 9

• Metropolis algorithm
• Continuous time MC algorithm (n-fold way
  algorithm)

M. Novotny, PRL 74, 1 (1995).
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Cooling-heating cicles at constant rate r
T(t) T(0) r t
L 150
Spinodal temperature Tsp 0.715
Tc(q9) 1/ln(4) 0.72135
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Relaxation at Tsp lt T lt Tc

Tc 1/ln(4) 0.72135
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Average energy per spin
Relaxation function
?
Tc 1/ln(4) 0.72135
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Relaxation at 0 ltlt T lt Tsp
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Equilibration time distribution
Equilibration time ? e(?) e(8) lt ?(L,T)
multiple-peak structure for T lt T 0.6
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T 0.2
Coarsening
t L2.5
average domain size
t L2
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q 2, T 0 V. Spirin, P.L. Krapivsky and S.
Redner, PRE 65, 016119 (2001)
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L 300 T 0.2
e(t)
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Relaxation at T ltlt Tc
disordered state with finite life time ? 1/T
for T lt Tg 0.1 (q 9)
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L300, T0.08
e(t)
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e(t)
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Conclusions
coarsening glassy state striped states
coarsening Lifshitz striped states
coarsening
nucleation