Universal Finite-Size-Scaling Functions

Abstract

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions. Keywords: Universal Finite-Size-Scaling Function; Ising Model; Order-Parameter Probability Distribution Function.

8 pages, Figures are available at http://glimmung.phys.sci.osaka-u.ac.jp/kikuchi/preprints.html or they will be sent upon request by e-mail

Cited by in corpus (11)

• Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle
• Cluster Analysis and Finite-Size Scaling for Ising Spin Systems
• Universal Finite-size Scaling Functions with Exact Non-universal Metric Factors
• Exact partition functions of the Ising model on MxN planar lattices with periodic-aperiodic boundary conditions
• Boundary conditions and amplitude ratios for finite-size corrections of a one-dimensional quantum spin model
• Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters
• Shape Effects of Finite-Size Scaling Functions for Anisotropic Three-Dimensional Ising Models
• Large-scale calculation of ferromagnetic spin systems on the pyrochlore lattice
• Universal relations in the finite-size correction terms of two-dimensional Ising models
• Cumulant ratios and their scaling functions for Ising systems in strip geometries
• Cluster Analysis of the Ising Model and Universal Finite-Size Scaling