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1.
For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t
–(q)
when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1. 相似文献
2.
Anomalous Fourier’s Law and Long Range Correlations in a 1D Non-momentum Conserving Mechanical Model
We study by means of numerical simulations the velocity reversal model, a one-dimensional mechanical model of heat transport
introduced in 1985 by Ianiro and Lebowitz. Our numerical results indicate that this model, which does not conserve momentum,
exhibits nevertheless an anomalous Fourier’s law similar to the ones previously observed in momentum-conserving models. This
disagrees with what can be expected by solving the Boltzmann equation (BE) for this system. The pair correlation velocity
field also looks very different from the correlations usually seen in diffusive systems, and shares some similarity with those
of momentum-conserving heat transport models. 相似文献
3.
We obtain the exact probability exp[-LF([rho(x)])] of finding a macroscopic density profile rho(x) in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system L-->infinity. F, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, F is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in nonconvexity of F, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state. 相似文献
4.
L. de Arcangelis H. J. Herrmann M. Kolb René Thomas C. Amitrano L. Peliti M. Saber G. Weisbuch Sara A. Solla F. Bagnoli A. Francescato R. Livi S. Ruffo Pablo Tamayo Michel Droz Peter Jörg Plath S. Romano Yves Pomeau Stéphane Zaleski D. Stauffer Luciano R. da Silva Alex Hansen Stéphane Roux Antonio Coniglio B. Derrida Henrik Flyvbjerg Naeem Jan Dietrich Stauffer Peter Grassberger A. Zippelius K. E. Kurten Werner Krauth Jean -Pierre Nadal Marc Mézard Per Bak Chao Tang Itzhak Webman M. L. Martins H. F. V. Resende C. Tsallis A. C. N. Magalhaes 《Journal of statistical physics》1989,55(5-6):1333-1359
5.
The asymmetric exclusion model describes a system of particles hopping in a preferred direction with hard core repulsion. These particles can be thought of as charged particles in a field, as steps of an interface, as cars in a queue. Several exact results concerning the steady state of this system have been obtained recently. The solution consists of representing the weights of the configurations in the steady state as products of non-commuting matrices. 相似文献
6.
T. Bodineau B. Derrida V. Lecomte F. van Wijland 《Journal of statistical physics》2008,133(6):1013-1031
We obtain explicit expressions for the long range correlations in the ABC model and in diffusive models conditioned to produce
an atypical current of particles. In both cases, the two-point correlation functions allow one to detect the occurrence of
a phase transition as they become singular when the system approaches the transition. 相似文献
7.
8.
It is shown how the weak disorder expansion of the Liapunov exponents of a product of random matrices can be derived when the unperturbed matrices have two degenerate eigenvalues. The general expression of the Liapunov exponents at the lowest nontrivial order in disorder is given. 相似文献
9.
For the 1D fully asymmetric exclusion model with open boundary conditions, we calculate exactly the fluctuations of the current of particles. The method used is an extension of a matrix technique developed recently to describe the equatime steady-state properties for open boundary conditions and the diffusion constant for particles on a ring. We show how the fluctuations of the current are related to non-equal-time correlations. In the thermodynamic limit, our results agree with recent results of Ferrari and Fontes obtained by working directly in the infinite system. We also show that the fluctuations of the current become singular when the system undergoes a phase transition with discontinuities along the first-order transition line. 相似文献
10.
We develop two independent transfer matrix methods for the determination of the exponent in the two-dimensional, self-avoiding walk problem. Our first method is based on the calculation of the correlation length and uses conformal invariance. Our second method is based on the direct calculation of the moments of the order parameter distribution. Our results are in good agreement with the conjectured values. 相似文献