Slow relaxation in microcanonical warming of a Ising lattice |
| |
Authors: | E Agliari M Casartelli A Vezzani |
| |
Institution: | (1) Lyman Laboratory of Physics, Harvard University, MA 02138 Cambridge, USA |
| |
Abstract: | We study the warming process of a semi-infinite cylindrical Ising lattice initially ordered and coupled at the boundary to
a heat reservoir. The adoption of a proper microcanonical dynamics allows a detailed study of the time evolution of the system.
As expected, thermal propagation displays a diffusive character and the spatial correlations decay exponentially in the direction
orthogonal to the heat flow. However, we show that the approach to equilibrium presents an unexpected slow behavior. In particular,
when the thermostat is at infinite temperature, correlations decay to their asymptotic values by a power law. This can be
rephrased in terms of a correlation length vanishing logarithmically with time. At finite temperature, the approach to equilibrium
is also a power law, but the exponents depend on the temperature in a non-trivial way. This complex behavior could be explained
in terms of two dynamical regimes characterizing finite and infinite temperatures, respectively. When finite sizes are considered,
we evidence the emergence of a much more rapid equilibration, and this confirms that the microcanonical dynamics can be successfully
applied on finite structures. Indeed, the slowness exhibited by correlations in approaching the asymptotic values are expected
to be related to the presence of an unsteady heat flow in an infinite system. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|