Do crossover functions depend on the shape of the interaction profile?

We examine the crossover from classical to non-classical critical behaviour in two-dimensional systems with a one-component order parameter. Since the degree of universality of the corresponding crossover functions is still subject to debate, we try to induce non-universal effects by adding interactions with a second length scale. Although the crossover functions clearly depend on the range of the interactions, they turn out to be remarkably robust against further variation of the interaction profile. In particular, we find that the earlier observed non-monotonic crossover of the effective susceptibility exponent occurs for several qualitatively different shapes of this profile.Comment: 7 pages + 4 PostScript figures. Accepted for publication in Europhysics Letters. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

Critical properties of the three-dimensional equivalent-neighbor model and crossover scaling in finite systems

Accurate numerical results are presented for the three-dimensional equivalent-neighbor model on a cubic lattice, for twelve 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 52514, 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.Comment: Corrected shift of critical temperature and some typos. To appear in Phys. Rev. E. 18 pages RevTeX, including 10 EPS figures. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm

A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model

In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation and critical behaviour in the Ising model, one might check whether the breakdown of hyperscaling in the Ising model can also be intepreted as due to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the critical temperature T_c. Preliminary results suggest that the scenario is much more involved than expected due to the fact that the percolation variables behave differently on the two sides of T_c.Comment: Lattice2002(spin

Medium-range interactions and crossover to classical critical behavior

We study the crossover from Ising-like to classical critical behavior as a function of the range R of interactions. The power-law dependence on R of several critical amplitudes is calculated from renormalization theory. The results confirm the predictions of Mon and Binder, which were obtained from phenomenological scaling arguments. In addition, we calculate the range dependence of several corrections to scaling. We have tested the results in Monte Carlo simulations of two-dimensional systems with an extended range of interaction. An efficient Monte Carlo algorithm enabled us to carry out simulations for sufficiently large values of R, so that the theoretical predictions could actually be observed.Comment: 16 pages RevTeX, 8 PostScript figures. Uses epsf.sty. Also available as PostScript and PDF file at http://www.tn.tudelft.nl/tn/erikpubs.htm

Monte Carlo Renormalization Group Analysis of Lattice ϕ4\phi^4 Model in D=3,4D=3,4

We present a simple, sophisticated method to capture renormalization group flow in Monte Carlo simulation, which provides important information of critical phenomena. We applied the method to $D=3,4$ lattice $\phi^4$ model and obtained renormalization flow diagram which well reproduces theoretically predicted behavior of continuum $\phi^4$ model. We also show that the method can be easily applied to much more complicated models, such as frustrated spin models.Comment: 13 pages, revtex, 7 figures. v1:Submitted to PRE. v2:considerably reduced redundancy of presentation. v3:final version to appear in Phys.Rev.

Universality class of criticality in the restricted primitive model electrolyte

The 1:1 equisized hard-sphere electrolyte or restricted primitive model has been simulated via grand-canonical fine-discretization Monte Carlo. Newly devised unbiased finite-size extrapolation methods using temperature-density, (T, rho), loci of inflections, Q = ^2/ maxima, canonical and C_V criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with potentials phi(r)>Phi/r^{4.9} when r \to \infty

Finite-size Scaling and Universality above the Upper Critical Dimensionality

According to renormalization theory, Ising systems above their upper critical dimensionality d_u = 4 have classical critical behavior and the ratio of magnetization moments Q = ^2 / has the universal value 0.456947... However, Monte Carlo simulations of d = 5 Ising models have been reported which yield strikingly different results, suggesting that the renormalization scenario is incorrect. We investigate this issue by simulation of a more general model in which d_u < 4, and a careful analysis of the corrections to scaling. Our results are in a perfect agreement with the renormalization theory and provide an explanation of the discrepancy mentioned.Comment: 5 pages RevTeX, 1 PostScript figure. Accepted for publication in Physical Review Letter

Screening in Ionic Systems: Simulations for the Lebowitz Length

Simulations of the Lebowitz length, $\xi_{\text{L}}(T,\rho)$, are reported for t he restricted primitive model hard-core (diameter $a$) 1:1 electrolyte for densi ties $\rho\lesssim 4\rho_c$ and $T_c \lesssim T \lesssim 40T_c$. Finite-size eff ects are elucidated for the charge fluctuations in various subdomains that serve to evaluate $\xi_{\text{L}}$. On extrapolation to the bulk limit for $T\gtrsim 10T_c$ the low-density expansions (Bekiranov and Fisher, 1998) are seen to fail badly when $\rho > {1/10}\rho_c$ (with $\rho_c a^3 \simeq 0.08$). At highe r densities $\xi_{\text{L}}$ rises above the Debye length, \xi_{\text{D}} \prop to \sqrt{T/\rho}, by 10-30% (upto $\rho\simeq 1.3\rho_c$); the variation is portrayed fairly well by generalized Debye-H\"{u}ckel theory (Lee and Fisher, 19 96). On approaching criticality at fixed $\rho$ or fixed $T$, $\xi_{\text{L}}(T, \rho)$ remains finite with $\xi_{\text{L}}^c \simeq 0.30 a \simeq 1.3 \xi_{\text {D}}^c$ but displays a weak entropy-like singularity.Comment: 4 pages 5 figure

Quantum spin chains with site dissipation

We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with the predictions from a dissipative $\phi^4$ field theory

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, that corresponds to the limit $N\to 0$ of an $N$-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions concerning the critical crossover functions, finding a good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal lscrossover behavior of our data for any finite range.Comment: 43 pages, revte