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Correlations in the motion of reptating polymers in a melt are investigated by means of Monte Carlo simulations of the three-dimensional slithering-snake version of the bond-fluctuation model. Surprisingly, the slithering-snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (created either by chain length N or by the volume fraction phi of occupied lattice sites), where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound tau+(N) is set by the density of chain ends phi/N. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of "snakes" at t<
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We demonstrate that the scaled order parameter for ferromagnetic Ising and three-state Potts chains with inverse square interactions exhibits a universal critical jump, in analogy with the superfluid density in helium films. Renormalization-group arguments are combined with numerical simulations of systems containing up to 10(6) lattice sites to accurately determine the critical properties of these models. In strong contrast with earlier work, compelling quantitative evidence for the Kosterlitz-Thouless-like character of the phase transition is provided.
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We consider d-dimensional systems with nonintegrable, algebraically decaying pairwise interactions. It is shown that, upon the introduction of periodic boundary conditions and a long-distance cutoff in the interaction range, the bulk thermodynamics can be obtained rigorously by means of a Kac-potential treatment, leading to an exact, mean-field-like theory. This explains various numerical results recently obtained for finite systems in the context of "nonextensive thermodynamics," and in passing exposes a strong regulator dependence not discussed in these studies. Our findings imply that, contrary to some claims, Boltzmann-Gibbs statistics are sufficient for a standard description of this class of nonintegrable interactions.
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We present a detailed discussion of the crossover from mean-field to Ising critical behavior upon approach of the critical point, both for 3He and Xe. By combining different sets of experimental data, we are able to cover an unusually large temperature range on either side of the critical temperature T(c). Below T(c), we thus can make an accurate comparison with a recent calculation for the crossover of the coexistence curve. For the regime above T(c), an analysis of the compressibility demonstrates that the crossover regime in 3He is unexpectedly widened by a subtle interplay between quantum and critical fluctuations.
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We discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long-range interactions. Although, since the introduction of the Luijten-Blote algorithm, Monte Carlo simulations of these systems no longer pose a fundamental problem, the energy calculation is still an O(N2) problem for systems of size N. We show how this can be reduced to an O(N log N) problem, with a break-even point that is already reached for very small systems. This allows the study of a variety of, until now hardly accessible, physical aspects of these systems. In particular, we combine the optimized energy calculation with histogram interpolation methods to investigate the specific heat of the Ising model and the first-order regime of the three-state Potts model with long-range interactions.
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Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for 12 different interaction ranges (coordination number between 18 and 250). These results allow the determination of the range dependences of the critical temperature and various critical amplitudes, which are compared to renormalization-group predictions. In addition, the analysis yields an estimate for the interaction range at which the leading corrections to scaling vanish for the spin-1 / 2 model, and confirms earlier conclusions that the leading Wegner correction must be negative for the three-dimensional (nearest-neighbor) Ising model. By complementing these results with Monte Carlo data for systems with coordination numbers as large as 52 514, the full finite-size crossover curves between classical and Ising-like behavior are obtained as a function of a generalized Ginzburg parameter. Also, the crossover function for the effective magnetic exponent is determined.
RESUMEN
We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously found for short-range interactions, this leads to a singular epsilon expansion, where epsilon is the distance to the upper critical dimension. Subsequently, we check the results by numerical simulations of spin models in the same universality class. Our systems offer the essential advantage that epsilon can be varied continuously, allowing an accurate examination of the region where epsilon is small. The numerical calculations turn out to be in striking disagreement with the predicted singularity.
