0000000000305259
AUTHOR
Henk W. J. Blöte
showing 5 related works from this author
Monte Carlo investigations of phase transitions: status and perspectives
2000
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.
Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
1999
Monte Carlo results for the moments of the magnetization distribution of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L \leq 22) is the linear dimension of a hypercubic lattice with periodic boundary conditions in d=5 dimensions, are analyzed in the critical region and compared to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod. Phys. C (1998)]. We show that this finite-size scaling theory (formulated in terms of two scaling variables) can account for the longstanding discrepancies between Monte Carlo results and the so-called ``lowest-mode'' theory, which uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature distan…
Nonmonotonical crossover of the effective susceptibility exponent
1997
We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly two orders of magnitude. The full crossover from classical to Ising-like critical behavior, spanning several decades in the reduced temperature, could be observed. Our results convincingly show that the effective susceptibility exponent gamma_eff changes nonmonotonically from its classical to its Ising value when approaching the critical point in the ordered phase. In the disordered phase the behavior is monotonic. Furthermore the hypothesis that the crossover function is universal is supported.
Crossover scaling in two dimensions
1997
We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the reduced temperature as well as in the finite-size crossover variable, it has up to now largely evaded a satisfactory numerical determination. Using a new Monte Carlo method, we could obtain accurate results for sufficiently large interactions ranges. Our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal. Also the so-called effective exponents are discussed …
Medium-range interactions and crossover to classical critical behavior
1996
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 …