The Universal Amplitude Ratio ${\Gamma }^{-}/{\Gamma }^{+}$ for Two-Dimensional Percolation

Abstract

The amplitude ratio of the susceptibility (or second size-moment) for two-dimensional percolation is calculated by two series methods and also by Monte-Carlo simulation. The first series method is a new approach based upon integrating approximations to the scaling function. The second series method directly uses low- and high-density series expansions of the susceptibility, going to unprecedented orders for both bond and site percolation on the square lattice. Putting all methods together we find a consistent value ${\Gamma }^{-}/{\Gamma }^{+}=162.5\pm 2$, a significant improvement over previous results that placed the value of this ratio variously in the range of 14 to 220.

4 pages, 3 figures

References in corpus (9)

• Efficient Monte Carlo algorithm and high-precision results for percolation
• Integrable field theory and critical phenomena. The Ising model in a magnetic field
• Universal amplitude ratios in the two-dimensional $q$-state Potts model and percolation from quantum field theory
• Universal ratios along a line of critical points. The Ashkin--Teller model
• Universal Amplitude Ratios of The Renormalization Group: Two-Dimensional Tricritical Ising Model
• Susceptibility amplitude ratios in the two-dimensional Potts model and percolation
• The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model
• Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase
• A universal amplitude ratio for the q<4 Potts model from a solvable lattice model

Cited by in corpus (5)

• Fields, particles and universality in two dimensions
• Universal amplitude ratios of two-dimensional percolation from field theory
• Stacked triangular lattice: Percolation properties
• High-temperature series expansions for the $q$-state Potts model on a hypercubic lattice and critical properties of percolation
• Finite-size corrections for logarithmic representations in critical dense polymers