Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models
1999; American Physical Society; Volume: 82; Issue: 20 Linguagem: Inglês
10.1103/physrevlett.82.3944
ISSN1092-0145
AutoresCharles M. Newman, D. L. Stein,
Tópico(s)Complex Network Analysis Techniques
ResumoA ``persistence'' exponent $\ensuremath{\theta}$ has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: For zero-temperature homogeneous Ising models on the $d$-dimensional cubic lattice ${Z}^{d}$, the fraction $p(t)$ of spins not flipped by time $t$ decays to zero like ${t}^{\ensuremath{-}\ensuremath{\theta}(d)}$ for low $d$; for high $d$, $p(t)$ may decay to $p(\ensuremath{\infty})>0$, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of the lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low $d$, and then present two examples---one disordered and one homogeneous---where $p(t)$ decays exponentially to $p(\ensuremath{\infty})$.
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