108 research outputs found
Crossover critical behavior in the three-dimensional Ising model
The character of critical behavior in physical systems depends on the range
of interactions. In the limit of infinite range of the interactions, systems
will exhibit mean-field critical behavior, i.e., critical behavior not affected
by fluctuations of the order parameter. If the interaction range is finite, the
critical behavior asymptotically close to the critical point is determined by
fluctuations and the actual critical behavior depends on the particular
universality class. A variety of systems, including fluids and anisotropic
ferromagnets, belongs to the three-dimensional Ising universality class. Recent
numerical studies of Ising models with different interaction ranges have
revealed a spectacular crossover between the asymptotic fluctuation-induced
critical behavior and mean-field-type critical behavior. In this work, we
compare these numerical results with a crossover Landau model based on
renormalization-group matching. For this purpose we consider an application of
the crossover Landau model to the three-dimensional Ising model without fitting
to any adjustable parameters. The crossover behavior of the critical
susceptibility and of the order parameter is analyzed over a broad range (ten
orders) of the scaled distance to the critical temperature. The dependence of
the coupling constant on the interaction range, governing the crossover
critical behavior, is discussedComment: 10 pages in two-column format including 9 figures and 1 table.
Submitted to J. Stat. Phys. in honor of M. E. Fisher's 70th birthda
Thermal Conductivity of Supercooled Water
The heat capacity of supercooled water, measured down to -37 {\deg}C, shows
an anomalous increase as temperature decreases. The thermal diffusivity, i. e.,
the ratio of the thermal conductivity and the heat capacity per unit volume,
shows a decrease. These anomalies may be associated with a hypothetical
liquid-liquid critical point in supercooled water below the line of homogeneous
nucleation. However, while the thermal conductivity is known to diverge at the
vapor-liquid critical point due to critical density fluctuations, the thermal
conductivity of supercooled water, calculated as the product of thermal
diffusivity and heat capacity, does not show any sign of such an anomaly. We
have used mode-coupling theory to investigate the possible effect of critical
fluctuations on the thermal conductivity of supercooled water, and found that
indeed any critical thermal-conductivity enhancement would be too small to be
measurable at experimentally accessible temperatures. Moreover, the behavior of
thermal conductivity can be explained by the observed anomalies of the
thermodynamic properties. In particular, we show that thermal conductivity
should go through a minimum as temperature is decreased, as Kumar and Stanley
observed in the TIP5P model of water. We discuss physical reasons for the
striking difference between the behavior of thermal conductivity in water near
the vapor-liquid and liquid-liquid critical points.Comment: References added, typos corrected. Extrapolation for viscosity
improved; results essentially unchange
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