Critical parameters and universal amplitude ratios of two-dimensional spin-S Ising models using high- and low-temperature expansions

Abstract

For the study of Ising models of general spin S on the square lattice, we have combined our recently extended high-temperature expansions with the low-temperature expansions derived some time ago by Enting, Guttmann and Jensen. We have computed for the first time various critical parameters and improved the estimates of others. Moreover the properties of hyperscaling and of universality (spin S independence) of exponents and of various dimensionless amplitude combinations have been verified accurately. Assuming the validity of the lattice-lattice scaling, from our estimates of critical amplitudes for the square lattice we have also obtained estimates of the corresponding amplitudes for the spin S Ising model on the triangular, honeycomb, and kagome` lattices.

15 pages, latex, no figures, corrected two typos

References in corpus (15)

• Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus
• Critical universality and hyperscaling revisited for Ising models of general spin using extended high-temperature series
• Critical behaviour of the two-dimensional Ising susceptibility
• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
• Low-Temperature Series Expansions for the Spin-1 Ising Model
• Universal amplitude ratios in the two-dimensional Ising model
• Localization of thermal packets and metastable states in Sinai model
• A library of extended high-temperature expansions of basic observables for the spin S Ising models on two- and three-dimensional lattices
• The critical equation of state of the 2D Ising model
• Eleventh-Order Calculation of Green's Functions in the Ising Limit for Arbitrary Space-Time Dimension $D$
• A Connection Between Complex-Temperature Properties of the 1D and 2D Spin $s$ Ising Model
• Zeros of the Partition Function for Higher--Spin 2D Ising Models
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Low temperature series expansions for the square lattice Ising model with spin S > 1
• Critical renormalized coupling constants in the symmetric phase of the Ising models

Cited by in corpus (9)

• The ϕ_3^4 lattice field theory viewed from the high-temperature side
• Finite-size scaling behavior in trapped systems
• Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions
• Universal Reduction of Effective Coordination Number in the Quasi-One-Dimensional Ising Model
• Spin-s Spin-Glass Phases in the d=3 Ising Model
• Universal and non-universal amplitude ratios for scaling corrections on Ising strips
• Second-order critical lines of spin-S Ising models in a splitting field with Grassmann techniques
• Sensitivity of the thermodynamics of two-dimensional systems towards the topological classes of their surfaces
• Quantum correlations versus spin magnitude: Transition to the classical limit