Multicanonical analysis of the plaquette-only gonihedric Ising model and its dual

The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of 0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension, 0.12037(18), using the statistics of suppressed configurations

Dynamic scaling of the restoration of rotational symmetry in Heisenberg quantum antiferromagnets

We apply imaginary-time evolution, ${\rm e}^{-\tau H}$, to study relaxation dynamics of gapless quantum antiferromagnets described by the spin-rotation invariant Heisenberg Hamiltonian ($H$). Using quantum Monte Carlo simulations, we propagate an initial state with maximal order parameter $m^z_s$ (the staggered magnetization) in the $z$ spin direction and monitor the expectation value $\langle m^z_s\rangle$ as a function of the time $\tau$. Different system sizes of lengths $L$ exhibit an initial size-independent relaxation of $\langle m^z_s\rangle$ toward its value the spontaneously symmetry-broken state, followed by a size-dependent final decay to zero. We develop a generic finite-size scaling theory which shows that the relaxation time diverges asymptotically as $L^z$ where $z$ is the dynamic exponent of the low energy excitations. We use the scaling theory to develop a way of extracting the dynamic exponent from the numerical finite-size data. We apply the method to spin-$1/2$ Heisenberg antiferromagnets on two different lattice geometries; the two-dimensional (2D) square lattice as well as a site-diluted square lattice at the percolation threshold. In the 2D case we obtain $z=2.001(5)$, which is consistent with the known value $z=2$, while for the site-dilutes lattice we find $z=3.90(1)$. This is an improvement on previous estimates of $z\approx 3.7$. The scaling results also show a fundamental difference between the two cases: In the 2D system the data can be collapsed onto a common scaling function even when $\langle m^z_s\rangle$ is relatively large, reflecting the Anderson tower of quantum rotor states with a common dynamic exponent $z=2$. For the diluted lattice, the scaling works only for small $\langle m^z_s\rangle$, indicating a mixture of different relaxation time scaling between the low energy states

Mesoscopic constitutive relations for dilute polymer solutions

A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system is taken to be a function of the position and velocity of the molecules, and on a local vector parameter accounting for its deformation. This function obeys a generalized Fokker-Planck equation, obtained by calculating the entropy production of the system, and identifying the corresponding probability currents in terms of generalized forces. In simple form, this coarse-grained description allows one to derive hydrodynamic equations where molecular deformation and diffusion effects are coupled. A class of non-linear constitutive relations for the pressure tensor are obtained. Particular models are considered and compared with experiments.Comment: To be published in Physica A (16 pages, 2 figures

Additivity property and emergence of power laws in nonequilibrium steady states

We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the distribution functions and the associated exponents. The asymptotic behavior of these distributions is solely governed by branch-cut singularity in the variance of subsystem mass. To substantiate these claims, we explicitly calculate, using the additivity property, subsystem mass distributions in a wide class of previously studied mass aggregation models as well as in their variants. These results could help in the thermodynamic characterization of nonequilibrium critical phenomena.Comment: Revised longer version, 4 figure