Monte Carlo investigations of phase transitions: status and perspectives

Abstract

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.

23 pages, including 14 PostScript figures. Presented at StatPhys-Taiwan, August 9-16, 1999. Also available as PDF file at http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.html

References in corpus (5)

• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• Nature of crossover from classical to Ising-like critical behavior
• Critical properties of the three-dimensional equivalent-neighbor model and crossover scaling in finite systems
• Shape of crossover between mean-field and asymptotic critical behavior in a three-dimensional Ising lattice
• Do crossover functions depend on the shape of the interaction profile?

Cited by in corpus (15)

• Hyperscaling above the upper critical dimension
• Finite Size Scaling for O(N) phi^4-Theory at the Upper Critical Dimension
• Classical-to-critical crossovers from field theory
• Scaling at quantum phase transitions above the upper critical dimension
• Critical behavior of the Coulomb-glass model in the zero-disorder limit: Ising universality in a system with long-range interactions
• Fast Flat-Histogram Method for Generalized Spin Models
• Universality and nonmonotonic finite-size effects above the upper critical dimension
• Active polar flock with birth and death
• Two-parameter scaling of correlation functions near continuous phase transitions
• Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps
• Binder cumulants of an urn model and Ising model above critical dimension
• Logarithmic finite-size scaling of the self-avoiding walk at four dimensions
• Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the hyperscaling violation
• Phase transitions above the upper critical dimension
• On a previously unpublished work with Ralph Kenna